s\ ^^^
REPORT
OF THE
FIFTYFIFTH MEETING
OP THE
BRITISH ASSOCIATION
FOR THE
ADVMCEMENT OF SCIENCE;
HELD AT
ABERDEEN IN SEPTEMBER 1885.
LONDON :
JOHN MURRAY, ALBEMARLE STREET.
1886.
Office of tne Association : 22 Albemarle Steeet, London, W.
PRINTED BY
8P0TTI8W00DE AND CO., NEWSTEBET SQUARE
LONDO.V
CONTENTS.
Page
Objects and Rules of the Association xxyii
Places and Times of Meeting and Officers from commencement xxxy i
Presidents and Secretaries of the Sections of the Association from com
mencement xUii
Evening Lectures Ivii
Lectures to the Operative Classes Ix
Officers of Sectional Committees present at the Aberdeen Meeting Ixi
Treasurer's Account Ixiii
Table showing the Attendance and Receipts at the Annual Meetings Ixiv
Officers and Council, 188586 Ixvi
Report of the Council to the General Committee livii
Tlecommendations adopted by the General Committee for Additional
Reports and Researches in Science Ixxi
Synopsis of Grants of Money Ixxix
Places of Meeting in 1886 and 1887 Ixxx
jeneral Statement of Sums which have been paid on account of Grants
for Scientific Purposes Ixxxi
rrangement of theGeneral Meetings xcii
iddress by the President, the Right Hon. Sir Lyon Platfaie, K.C.B., M.P.,
F.R.S 1
*
EEPORTS ON THE STATE OF SCIENCE.
Report of the Committee, consisting of Professor G. Carey Foster, Sir W.
Thomson, Professor Ayrton, Professor J. Perry, Professor W. G. Adaks,
Lord Rayleigh, Dr. 0. J. LpDGE, Dr. John Hopkinson, Dr. A. Mtjirheab,
Mr. W. H. Preece, Mr. H. Taylor, Professor Everett, Professor Schus
ter, Dr. J. A. Fleming, Professor G. F. Fitzgerald, Mr. R. T. Glaze
brook (Secretary), Professor Chrystal, Mr. H. Tomlinson, and Professor
W. Garnett, appointed for the purpose of constructing and issuing practical
Standards for use in Electrical Jleasurements 31
Report of the Committee, consisting of Professors A. Johnson (Secretary), J.
G. MacGregoh, J. B. Cherriman, and H. T. Botey and Mr. C. Carpmael,
appointed for the purpose of promoting Tidal Observations in Canada 8u
A3
IV CONTENTS.
Page
Fifth Report of the Committee, consisting of Mr. John Murkat (Secretary),
Professor Schttster, Professor Sir William Thomson, Professor Sir H. E.
RoscoE, Professor A. S. IIerschel, Captain W. de W. Abnet, Professor
Bonnet, Mr. R. H. Scott, and Dr. J. H. Gladstone, appointed for the pur
pose of investigating the practicability of collecting and identifying Meteoric
Dust, and of considering the question of undertaking regular observations
in various localities 34
Third Report of the Committee, consisting of Professors G. H. Darwin and
J. C. Adams, for the Harmonic Analysis of Tidal Observations. Drawn
up by Professor G. H. Darwin 35
Report of the Committee, consisting of Mr. Robert H. Scott (Secretary),
Mr. J. Norman Lockter, Professor G. G. Stokes, Professor Balfour
Stewart, and Mr. G. J. Stmons, appointed for the purpose of cooperating
with the Meteorological Society of the Mauritius in their proposed publica
tion of Daily Synoptic Charts of the Indian Ocean from the year 1861.
Drawn up by Mr. R. H. Scott 60
Rejjort of the Committee, consisting of Mr. James N. Shoolbred (Secre
tary) and Sir William Thomson, appointed for the reduction and
tabulation of Tidal Observations in the English Channel, made with the
Dover Tidegauge ; and for connecting them with Observations made on the
French coast 60
Report of the Committee, consisting of Professor G. Forbes (Secretary),
Captaiu Abnet, Dr. J. IIopkinson, Professor W. G. Adams, Professor
G. C. Foster, Lord Ratleigh, Mr. Preece, Professor Schuster, Professor
Dewar, Mr. A. Veknon Harcourt, and Professor Atrton, appointed for
the purpose of reporting on Standards of "V\'hite Light. Drawn up by
Professor G. Forbes 61
Second Report of the Committee, consisting of Professor Balfour Stewart
(Secretary), Mr. J. Knox Laughton, Mr. G. J. Symons, Mr. R. H. Scott,
and Mr. Johnstone Stoney, appointed for the purpose of cooperating with
Mr. E. J. Lowe in his project of establishing a Meteorological Observatory
near Chepstow on a permanent and scientific basis 64
Report of the Committee, consisting of Professor Balfour Stewart
(Secretary), Sir W. Thomson, Sir J. H. Lefroy, Sir Frederick Evans,
Professor G. H. Darwin, Professor G. Chrystal, Professor S. J. Perry,
Mr. C. H. Caepmael, and Professor Schuster, appointed for the purpose of
considering the best means of Comparing and Reducing Magnetic Observa
tions. Drawn up by Professor Balfour Stewart 65
Report of the Committee, consisting of Professor Crum Brown (Secretary),
Mr. MiLNEHoME, Mr. John Murray, and Mr, Buchan, appointed for the
purpose of cooperating with the Scottish Meteorological Society in making
Meteorological Observations on Ben Nevis 90
Seventeenth Report of the Committee, consisting of Professor Everett, Pro
fessor Sir AV. Thomson, Mr. G. J. Symons, Sir A. C. Ramsay, Dr. A.
Geikib, Mr. J. Glaisher, Mr. Pengellt, Professor Edward Hull,
Professor Prestwich, Dr. C. Le Neve Foster, Professor A. S. Herschel,
Professor G. A. Lebour, Mr. Galloway, Mr. Joseph Dickinson, Mr. G. F.
Deacon, Mr. E. Wexhered, and Mr. A. Strahan, appointed for the
purpose of investigating the Rate of Increase of Underground Temperature
downwards in various Localities of Dry Land and under Water. Drawn
up by Professor Everett (Secretarj) 93
Report on Electrical Theories. By Professor J. J. Thomson, M.A., F.R.S — 97
Second Report of the Committee, consisting of Professor Schuster (Secretary),
Professor Balfour Stewart, Professor Stokes, Mr. G. Johnstone Sxoney,
Professor Sir H. E. RoscoE, Captain Abney, and Mr. G. J. Symons, ap
pointed for the purpose of considering the best methods of recording the
direct Intensity of Solar Radiation 56
CONTENTS. V
Page
Report on Optical Theories. By R. T. Glazebrook, M.A., F.R.S 157
Report of the Committee, consisting of Professors Ramsay, Tilden, Mar
shall, and W. L. Goodwin (Secretary), appointed for the purpose of
investigating certain Physical Constants of Solution, especially the Expan
sion of Saline Solutions 261
Third Report of tlie Committee, consisting of Professors Williamson, Dewar,
Feankland, Crum Brown, Obling, and Armstrong, Drs. Hugo Muller,
r. R. Japp, and H. Forster Morlex, and Messrs. A. G. Vernon Har
coFRT, C. E. Groves, J. Millar Thomson, H. B. Dixon (Secretary), and
V. H. Velet, reappointed for the purpose of drawing up a statement of
the varieties of Chemical Names which have come into use, for indicating
the causes which have led to their adoption, and for considering what can
be done to bring about some convergence of the views on Chemical Nomen
clature obtaining among English and foreign chemists 262
Report of the Committee, consisting of Professors Odling, Huntington, and
Hartley, appointed to investigate by means of Photography the Ultra
violet Spark Spectra emitted by Metallic Elements and their combinations
under varying conditions. Drawn up by Professor W. N. Hartley, F.R.S.
(Secretary) 276
Report of the Committee, consisting of Professor Tilden, Professor W.
Ramsay, and Dr. W. W. J. Nicol (Secretary), appointed for the purpose
of investigating the subject of Vapour Pressures and Refractive Indices of
Salt Solutions 284
Report of the Committee, consisting of Professor Sir H. E. Roscoe, Mr. J. N.
Lockyer, Professors Dewar, Wolcott Gibbs, Liveing, Schuster, and
W. N. Hartley, Captain Abney, and Dr. Marshall Watts (Secretary),
appointed for the purpose of preparing a new series of AVavelength Tables
of the Spectra of the Elements and Compounds 288
Thirteenth Report of the Committee, consisting of Professors J. Prestwich,
W. Boyd Dawkins, T. McK. Hughes, and T. G. Bonney, Dr. H. W.
Geosskey (Secretary), Dr. Deane, and Messrs. C. E. De Range, H. G.
FoRDHAM, J. E. Lee, D. Mackintosh, W. Pengelly, J. Plant, and R. H.
TiDDEMAN, appointed for the purpose of recording the position, height
above the sea, lithological characters, size, and origin of the Erratic Blocks
of England, Wales, and Ireland, reporting other matters of interest con
nected with the same, and taking measures for their preservation 322
Third Report of the Committee, consisting of Mr. R. Etheridge, Dr. H.
WooDAVARD, and Professor T. Rupert Jones (Secretary), on the Fossil
Phyllopoda of the Palaeozoic Rocks 326
Fifth Report of the Committee, consisting of Mr. R. Etheridge, Mr. Thomas
Gray, and Professor John Milne (Secretary), appointed for the purpose
of investigating the Earthquake Phenomena of Japan. Drawn up by the
Secretary 362
Eleventh Report of the Committee, consisting of Professor E. Hull, Dr.
H. W. Ceosskey, Captain Douglas Galton, Professors J. Pkesiwich
and G. A. Lebour, and Messrs. James Glaisher, E. B. Marten, G. H.
Morton, James Parker, W. Pengelly, James Plant, I. Roberts, Fox
Steangways, T. S. Stooke, G. J. Symons, W. Toplet, TyldenWright,
E. Wethered, W. Whitaker, and C. E. De Range (Secretary), ap
pointed for the purpose of investigating the Circulation of Underground
Waters in the Permeable Formations of England and Wales, and the
Quantity and Character of the Water supplied to various Towns and Dis
tricts from these Formations. Drawn up by C. E. De Range 380
VI CONTENTS.
Page
Eeport of the Committee, consisting of Mr. H. Batterman, Mr. F. AV.
Rtjdler, and Dr. H. J. JohnstonLavis, for the Investigation of the
Volcanic Plieuomena of Vesuvius. Drawn up by H. J. JohnstonLavis,
M.D., F.G.S. (Secretary) 395
Report of the Committee, consisting of i\L'. W. T. Blanfoed and Mr. J. S.
Gaedxer (Secretary), on the Fossil Plants of the Tertiary and Secondary
Beds of the United" Kingdom. Drawn up by Mr. J. S. Gaednee, F.G.S",
F.L.S 396
Report of the Committee, consisting of Messrs. R. B. Grantham, C. E. De
Rance, J. B. Redman, W. Toplet, W. Whitakee, and J. W. Woodall,
MajorGeneral Sir A. Claeke, Sir J. N. Douglass, Captain Sir F. 0. Evans,
Admiral Sir E. Ommanney, Captain J. Parsons, Professor J. Peestavicu,
Captain W. J. L. Whaeton, and Messrs. E. Easton, J. S. Valentine, and
L. F. Vernon Haecottrt, appointed for the purpose of inquiring into the
Rate of Erosion of the Seacoasts of England and Wales, and the Influence
of the Artificial Abstraction of Shingle or other Material in that Action.
0. E. De Rance and "W. Topley, Secretaries ; the Report edited by W.
Toplet 404
Report of the Committee, consisting of Professor Rat Lankester, Mr. P. L.
Sclater, Professor M. Foster, Mr. A. Sedgavick, Professor A. M. Mar
shall, Professor A. C. Haddon, Professor Moselet, and Mr. Peect
Sladen (Secretary), appointed for the purpose of arranging for the occu
pation of a Table at the Zoological Station at Naples 466'
Report of the Committee, consisting of Professor McIvendeick, Professor
Struthers, Professor Young, Professor McIntosh, Professor Alletne
Nicholson, Professor Cossar Ewaet, and Mr. John Mxjrrat (Secretary),
appointed for the purpose of promoting the establishment of a Marine
Biological Station at Granton, Scotland 474
Report of the Committee, consisting of Sir Lton Platfair, Professor IVIose
I.ET, Admiral Sir E. Ommanney, Mr. P. L. Sclater, and Mr. A. Sedgwick
(Secretary), appointed to prepare a Report on the Aid given by the Do
minion Government and the Government of the United States to the
encouragement of Fisheries, and to the investigation of the various forms
of Marine Life on the coasts and rivers of North America 479'
Report of the Committee, consisting of Professor Huxlet, Mr. Sclater,
Mr. Howard Saunders, Mr. Thiselton Dter, and Professor Moselet
(Secretary), appointed for the purpose of promoting the establishment of
Marine Biological Stations on the coast of the United Kingdom 480'
Report of the Committee, consisting of Dr. H. C. Soebt and Mr. G. R. Vine,
appointed for the purpose of reporting on recent Polyzoa. Drawn up by
Mi: G. R. Vine 481
Third Report of the Committee, consisting of Sir J. Hooeee, Dr. Qunthbr,
Mr. HowAED Saundees, and Mr. Sclatee (Secretary), appointed for the
purpose of exploring Kilimanjaro and the adjoining mountains of Equa
torial Africa 681
Report of the Committee, consisting of Mr. John Coedeaux (Secretary),
Professor A. Newton, Mr. J. A. HaevieBeown, Mr. William Eagle
Claeke, Mr. R. M. Barrington, and Mr. A. G. More, appointed for the
purpose of obtaining (with the consent of Master and Brethren of the
Trinity House and the Commissioners of Northern and Irish Lights)
observations on the Migration of Birds at Lighthouses and Ligh tvessels,
and of reporting on the same 685
CONTENTS. Vll
Page
Eeport of the Committee, consistiog of General Sir J. H. Lefrot, Lieut.
Colonel GoDWiNAtrsTEN, Mr. W. T. Blajiford, Mr. Sclater, Mr.
Carrtjthers, Mr. ThiseltonDter, Professor Struthers, Mr. G. W.
Bloxam, Mr. H. W. Bates (Secretary), Lord Alfred Ghtirchill,
ilr. F. Galton, and Professor Moselet, appointed for the puipose of
furthering the Exploration of New Guinea by making a grant to
Mr. Forbes for the purposes of his expedition 690
Report of the Committee, consisting of General Sir J. H. Lefrot, the Rev.
Canon Carver, Mr. F. Galton, Mr. P. L. Sclater, Professor Moselet,
Dr. E. B. Tilor, Professor Boyd Dawkins, Mr. G. W. Bloxam, and
Mr. H. W. Bates (Secretary), appointed for the purpose of furthering the
scientific examination of the country in the vicinity of Mount Roraima in
Guiana, by making a grant to Mr. Everard F. im Thurn for the purposes of
his expedition 6y0
Report of the Committee, consisting of the Rev. Canon Tristram, the
Rev. F. Lawrence, and Mr. James Glaisher (Secretary), appointed for
the purpose of promoting the Sur\ey of Palestine 691
Report of the Committee, consisting of Dr. J. H. Gladstone (Secretary),
Mr. William Shaen, Mr. Stephen Bourne, Miss Ltdia Becker, Sir
John Lubbock, Dr. H. "W. Crossket, Sir Richard Temple, Sir Henrt E.
RoscoE, Mr. James Hetwood, and Professor N. Stoet Maskeltne,
appointed for the purpose of continuing the inquiries relating to the
teachbg of Science in Elementary Schools 692
Report of the Committee, consisting of Sir Frederick Bramwell (Secre
tary), Professor A. "W. Williamson, Professor Sir William Thomson, Mr.
St. John Vincent Dat, Sir F. Abel, Captain Douglas Galton, Mi. E. H.
Carbutt, Mr. Macrort, Mr. H. Trueman Wood, Mr. W. H. Barlow,
Mr. A. T. Atchison, Sir R. E. Webster, Mr. A. Carpmael, Sir John
Lubbock, Mr. Theodore Aston, and Mr. James Brunlees, appointed for
the purpose of watcliing and reporting to the Council on Patent Legislation 695
Report of 4he Committee, consisting of Dr. E. B. Ttloe, Dr. G. M. Dawson,
General Sir J. H. Lefrot, Dr. Daniel Wilson, Mr. Horatio Hale,
Mr. R. G. Haliburton, and Mr. Georgse W. Bloxam (Secretary),
appointed for the pmpose of investigating and publishing reports on the
physical characters, languages, and industrial and social condition of the
Northwestern Tribes of the Dominion of Canada
Report to the Council of the Corresponding Societies Conxmittee, consistin"'
of Mr. Francis Galton (Chairman), Professor A. W. Williamson^
Captain Douglas Galton, Professor Botd Dawkins, Sir Rawson Rawson,
Dr. Gakson, Dr. J. Evans, Mr. J. Hopkinson, Professor Meldola
(Secretary), Mr. W^hitaker, Mr. G. J. Stmons, and Mr. H. George
Fobdham 708
On Electrolysis. By Professor Oliver J. Lodge, D.Sc 723
A Tabular Statement of the Dates at which, and the Localities where,
Pumice or Volcanic Dust was seen in the Lidian Ocean in 188384. By
Charles Meldeum, F.R.S 773
List of Works on the Geology, Mineralogy, and Palseontology of Stafford
shire, Worcestershire, and Warvriickshire. By William Whitaker, B.A.,
F.G.S., Assoc.Inst.C.E 780
On Slaty Cleavage and allied RockStructures, with special reference to the
Mechanical Theories of theii Origin. By Alfred Harkeb, M.A., F.G.S. ^^'^
VUl CONTENTS.
Page
On the Strength of Telegraph Poles. By W. H. Preece, F.E.S.,
M.Inst.O.E 853
On the Use of Index Numbers in the Investigation of Trade Statistics. By
Stephen Bourne, F.S.S 859
The Forth Bridge Works. By Andrew S. Biggart, C.E 873
Electric Lighting at the Forth Bridge Works. By James N. Shoolbred,
B.A., M.Inst.O.E 879
The New Tay Viaduct. By Crawford Barlow, B.A., M.InstO.E 883
TEANSACTIONS OF THE SECTIONS.
Section A.— MATHEMATICAL AND PHYSICAL SCIENCE.
THURSDAY, SEPTEMBER 10.
Page
Address bj Professor G. Chrtstal, M.A., F.R.S.E., President of the Section 889
1. On the Dilatancy of Media composed of Eigid Particles in Contact. By
Professor Osborne Reynolds, M.A., F.R.S 896
2. On Calculating the Surface Tension of Liquids by means of Cylindrical
Drops or Bubbles. By Professor G. PiRiE, M.A 898
3. On the Suiface Tension of Water which contains a Gas dissolved ia it.
By Professor G. Pieie, M.A 898
4. Thermod\namic Efficiency of Thermopiles. By Lord Ratleigf, D.C.L.,
LL.D., F.R.S 898
6. On the Measmement of the Intensity of the Horizontal Component of the
Earth's Magnetic Field. By Thomas Gray, B.Sc, F.R.S.E 898
6. On Atmospheric Electricity. By Professor C. Michie Smith, B.Sc,
F.R.S.E 899
7. Molecular Distances in Galvanic Polarisation. By Professor J. Larmor,
M.A 900
8. On the Employment of Mance's Method for eliminating the Effects of
Polarisation, to determine the Resistance of the Human Body. Bv Dr.
W. H. SxoNE, M.A .' 900
9. On Contact Electricity in Common Air, Vacuum, and different Gases. By
J. T. BoTTOMLEY, M.A., F.R.S.E 901
10. On a Specimen of almost Unmagnetisable Steel. By J. T. Bottomlet,
M.A., F.R.S.E 903
11. On the Cooling of Wires in Air and in Vacuum. By J. T. Bottomlet,
M.A., F.R.S.E 904
FBIDAY, SEPTEMBER 11.
1. On Kinetic Theories of Matter. By Professor A. CRinu: Brown,
M.D., F.R.S 904
2. On Kinetic Theories. By Professor G. D. Liveing, M.A., F.R.S 904
3. On Thermal Effusion and the Limiting Pressure in Polarised Gas. By
G. JoHNSTONi! Stoney, LL.D., F.R.S 904
4. On a Law concerning Radiation. By Professor Schuster, Ph.D., F.R.S. 905
5. On Boltzmaun's Theorem. By Professor W. M. Hicks, M.A., F.R.S. ... 905
X co:ntEiNts.
Page
6. The Rate of Explosion of Hydrogen and Oxygen. By H. B. Dixon, M.A. 905
7. Report of the Committee for constructing and issuing practical Standards
for use in Electrical Measurements 905
8. Report on Electrical Theories. By Professor J. J. Thomson, M.A., F.R.S. 905
9. On Constant Gravitational Instruments for measuring Electric Currents
and Potentials. By Professor Sir W. Thomson, LL.D., F.R.S 905
10. On a method of multiplying Potential from a hundred to several thousand
Volts. By Professor Sir William ThomsOxV, LL.D., F.R.S 907
11. On a form of Mercury Contact Commutator of Constant Resistance for use
in adjusting Resistance Coils by Wheatstone's Bridge, and for other
purposes. By Professor J. Viriamu Jones 907
12. On Slide Resistance Coils with ftlercury Contacts. By Professor J.
ViBiAMTT Jones 907
13. On the relative Merits of Iron and Copper Wire for Telegraph Lines. By
W. H. Peeece, F.R.S 907
SATURDAY, SEPTEMBER 12.
1. On Orthoptic Loci. By the Rev. C. Taylor, D.D 909
2. On the Reduction of Algebraical Determinants. By "\V. H. L. Russell,
F.R.S 910
3. Account of the Levelling Operations of the Great Trigonometrical Survey
of India. By Major A. W. Baikd, R.E., F.R.S 911
4. A Theorem relating to the Timemoduli of Dissipative Systems. By Lord
Ratleigh, D.C.L., LL.D., F.R.S 911
5. On a new Polariser devised by Mr. AJirens. By Professor Silvanits P.
Thompson, D.Sc 912
6. On a simple Modification of the Nicol Prism giving "Wider Angle of Field.
By Professor Silvanus P. Thompson, D.Sc 912
7. On some of the Laws which regulate the Sequence of Mean Temperature
and Rainfall in the Climate of London. By II. Coitrtenat Fox, M.R.C.S. 912
8. Notes upon the Rotational Period of the Earth and Revolution Period of
the Moon deduced from the Nebular Hypothesis of Laplace. By W. F.
Stanley, F.G.S., F.R.M.S 915
9. On a Galvanic Battery. By C. J. Burnett 916
MONDAY, SEPTEMBER U.
1. Report of the Committee on Standards of White Light 916
2. Photometry with the Pentane Standard. By A. Vernon Harcouet,
M.A., F.R.S 916
3. On a Photometer made with Translucent Prisms. By J. Joly, B.E 917
4. Report of the Committee for reducing and tabulating the Tidal Obser
vations in the English Channel, made with the Dover Tidegauge ; and
for connecting them with Observations made on the French coast 917^
5. Seventeenth Report of the Committee on Underground Temperature 917
6. Fifth Report of the Committee on Meteoric Dust 917
7. A Tabular Statement of the Dates at which, and the Localities where,
Pumice or Volcanic Dust was seen in the Indian Ocean in 188384. By
Charles Meldrum, F.R.S 917"
CONTENTS. xi
8. Eeport of the Committee for cooperating with the Meteorological Society
of the Mauritius in their proposed publication of Daily Synoptic Charts
of the Indian Ocean from the year 1861 917
9. Daily Synoptic Charts of the Indian Ocean. By Charles Meldexjjt, F.E.S. 917
10. Eeport of the Committee appointed to cooperate with the Scottish
Meteorological Society in making Meteorological Observations on Ben
Nevis
917
11. On the Meteorology of Ben Xevis. By Alexander Buchan 917
12. On some Eesults of Observations with kitewiresuspended Anemometers
up to 1,300 feet above ground, or 1,800 feet above sealevel, in 188385.
By E. Douglas Archibald 9^9
13. On the Measurement of the Movements of the Ground, with reference to
proposed Earthquake Observations on Ben Nevis. Bv Professor J \
EwiNG, B.Sc, F.E.S.E \' ' 920
14. On the supposed Change of Climate in the British Isles within recent
years. By Thomas Heath,B.A 922
15. On Malvern, Queen of Inland Health Eesorts, and on improved Hygro
metric Observations. By Professor C. Piazzi Smyth, F.E.S.E 922
16. The Annual Eainfall of the British Islands. By Alexander Buchan ... 923
17. Eemarkable Occurrence during the Thunderstorm of August 6, 1885, at
Albrighton. By J. Bedford Elwell ? .',.., 924
18. On a supposed Periodicity of the Cyclones of the Indian Ocean south of
the Equator. By Charles Meldrum, F.E.S 926
19. A new Wind Vane or Anemoscope, specially designed for the use of
Meteorologists. By G. M. Whipple, B.Sc, F.E.A.S 926
■ 20. On the Third Magnetic Survey of Scotland. By Professor T. E. Thorpe
F.E.S., and A. W. Eucker, F.E.S ' 926
TUESDAY, SEPTEMBER 15.
1. Eeport of the Cormnittee for considering the best means of Comparing
and Eeducing Magnetic Observations 928
2. Eeport of the Committee for considering the best methods of recordino
the direct Intensity of Solar Eadiation ° 923
3. On a means of obtaining constant known Temperatures. By Professor
W. Eamsat, Ph.D., and Sydney Young, D.Sc 928
4. On certain facts in Thermodynamics. By Professor W Eamsay Ph D
and Sydney Young, D.Sc ' '928
5. Eeport on Optical Theories. By E. T. Glazebrooe:, M.A., F.E.S 929
6. On a Point in the Theory of Double Eefraction. By E. T. Glazebrook,
M.A., F.E.S 929
7. Exhibition of a Mechanical Model illustrating some propert'es of the
Ether. By G. F. Fitzgerald, F.E.S 93O
8. On the Constitution of the Luminiferous Ether on the Vortex Atom
Theory. By Professor W. M. Hices, M.A., F.E.S 930
9. On an improved Apparatus for Christiansen's Experiment. Bv Lord
Eayleigh, D.C.L., LL.D., F.E.S 930
10. Optical Comparison of Methods for observing small Eotations Bv Lord
Eayleigh, D.C.L., LL.D., F.E.S 930
11. On the Accuracy of Focus necessary for sensibly perfect Definition Bv
Lord Eayleigh, D.C.L., LL.D., F.E.S .'....... 930
XU CONTENTS
Page
12. On ElectroOptic Action of a Charged Franklin's Plate. By J. Kerb,
LL.D 930
13. On Magnetic Double Circular Refraction. By De Witt B. Brace, Ph.D. 931
14. Determination of the Heliographic Latitude and Longitude of Sunspots.
By Professor A. W. Thomson 931
WEDXESDAT, SEPTEMBER 16.
1. On the Nature of the Corona of the Sun. By William Huqgins, D.C.L.,
LL.D., F.R.S 932
2. On the Spectrum of the SteUa Nova visible on the Great Nebula in An
dromeda. By William HuGsiNs, D.C.L., LL.D., F.R.S 935
3. On the Bright Star iu the Great Nebula in Andromeda. By Ralph
COPELAND, Ph.D 935
4. On Solar Spectroscopy in the Infra Red. By Dr. Daniel Draper 936
^. The Errors of Sextants as indicated by the Records of the Verification
Department of the Kew Observatory, Richmond, Surrey. By G. M.
Whipple, B.Sc, F.R.A.S ". 936
6. On the Behaviour of Firstclass Watches whilst undergoing tests in the
Rating Department of the Kew Observator}, Richmond, Surrey. By G.
M. Whipple, B.Sc, F.R.A.S 937
7. On a recent Improvement in the Construction of Instruments graduated
upon Glass. By G. M. Whipple, B.Sc, F.R.A.S 937
8. On Methods of preventing Change of Zero of Thermometers by Age. By
G. M. Whipple, B.Sc, F.R.A.S 938
9. On a new and simple form of Calorimeter. By Professor W. F. Barrett 938
10. On a modification of the Dauiell Battery, using Iron as Electropositive
Element. By J. J. Coleman 938
11. On a new form of Galvanometer. By Professor James Bltth, M.A.,
F.R.S.E 939
12. On the Physical Conditions of Water in Estuaries. By Hugh Robert
Mill, B.Sc, F.R.S.E., F.C.S 940
13. Further Experiments in PhotoElectricity. By Professor Minchin 940
14. On the Formation of a Puie Spectrum by Newton. By G. Griffith,
M.A 940
16. On the Use of Bisulphide of Carbon Prisms for cases of Extreme Spectro
scopic Dispersion, by Professor C. Piazzi Smyth ; and their Results in
Gaseous Spectra, commented on by Professor Alexander S. IIerschel,
M.A., F.R.S 942
Section B.— CHEMICAL SCIENCE.
THURSDAT, SEPTEMBER 10.
Address by Professor H. E. Armstrong, Ph.D., F.R.S., Sec.C.S., President
of the Section 946
1. Report of the Committee appointed for the purpose of investigating by
means of Photography the Ultra Violet Spark Spectra emitted by Metallic
Elements and their combinations under varying conditions 965
2. On the Nonexistence of Gaseous Nitrous Anhydride. By Professor
William Ramsay, Ph.D., and J. Tudor Cundall 965
CONTENTS. Xlll
Page
3. On some Actions of a Groves's Gasbattery. By Professor William
Kamsat, Ph.D 965
4. On the Spontaneous Polymerisation of Volatile Hydrocarbons at tlie
ordinary atmospheric temperature. By Professor Sir Henet E. Roscoe,
F.R.S.1 967
5. On some new Vanadium Compounds. By J. T. Brieelet 968
FRIDAY, SEPTEMBER 11.
1. On the Essential Elements of Plants. By T. Jamieson 969
2. The Periodic Law, as illustrated by certain physical properties of Organic
Compounds. By Professor Thos. Caenellt, D.Sc 969^
3. Suggestions as to the Cause of the Periodic Law and the Nature of the
Chemical Elements. By Professor Thos. Caenellt, D.Sc 969
4. On the Value of the Refraction Goniometer in Chemical work. By Dr.
J. H. Gladstone, F.R.S 970
5. On the Refraction of Fluorine. By Geoege Glabstone, F.C.S 970
6. Note on some Conditions of the Development, and of the Activity, of
Chlorophyll. By Profe.ssor J, H. Gilbebt, LL.D., F.R.S 970
7. A Plea for the Empiric Naming of Organic Compounds. By Professor
Odling, F.R.S 972
8. On the Action of Sodium Alcoholates on Fumaric and Maleic Ethers. By
Professor Pttrdie, Ph.D., B.Sc 972
9. On Sulphine Salts derived from Ethylene Sulphide. By Okste Masson,
M.A., D.Sc 974
10. An apparently new Hydrocarbon distilled from Japanese Petroleimi. By
Dr. DivEES and T. Nakamuea 975
11. Description of some new Crystallised Combinations of Copper, Zinc, and
Iron Sulphates. By John Spillee, F.C.S 976
SATURDAY, SEPTEMBER 12.
1. The Composition of Water by Volume. By A. Scott, M.A., D.Sc
F.R.S.E 976
2. Description of a new Mineral from Loch Bhruithaich, Invernessshire.
By W, IvisoN Macadam, F.C.S., and Thomas Wallace 977
3. Exhibition and Description of the apparatus employed in obtaining Oxygen
and Nitrogen from the Atmosphere. Description of method used in
converting Atmospheric Nitrogen into Ammonia. By Messrs. Bein
Brothers 977
MONDAY, SEPTEMBER 14.
1. Report of the Committee on Chemical Nomenclature 977
2. On Electrolysis. By Professor Olivee J. Lodge, D.Sc 977
3. On Helmholtz's views on Electrolysis, and on the Electrolysis of Gases.
By Professor Schustee, F.R.S 977
4. On the Determination of Chemical Affinity in terms of Electromotive
Force. By 0. R. Aldee Weight, D.Sc, F.R.S 973.
o. On the Sensitiveness to Light of Selenium and Sulphur Cells. By Shel
EOED BiDWELL, M.A., LL.B 98L
Xiv CONTENTS.
Page
6. On the Generation of a Voltaic Current by a Sulphur Cell with a Solid
Electrolyte. By Shelford Bidwell, M.A., LL.B 982
7. A Theory of the Connection between the Crystal Form and the Atom
Composition of Chemical Compounds. By William Baelow 983
S. On the use of Sodium or other soluble aluminates for softening and purify
ing bard and impure water and deodorising and precipitating sewage,
waste water from factories, &c. By F. Maxwell Ltte, F.C.S 984
TUESDAY, SEPTEMBER 15.
1. Report on Vapour Pressures and Refractive Indices of Salt Solutions 985
2. Report on certain Physical Constants of Solution 985
3. On Solutions of Ozoue and the Chemical Actions of Liquid Oxygen. Bv
Professor Dewak, F.R.S .". 985
4. On Physical Molecular Equivalents. By Professor Guthrie, F.R.S 985
5. The Size of Molecules. By Professor A. W. Reinold, M.A., F.R.S 986
6. An approximate determination of the Absolute. Amounts of the Weights
of the Chemical Atoms. By G. Johnstone Stoxet, D.Sc, F.R.S 987
7. On Macromolecules (^lolecules of Matter in the CJrystalline State as dis
tinct from the Chemical Molecule), and determinations of some of them.
By G. Johnstone Stonet, D.Sc, F.R.S 988
8. On the Dilatancy of Media composed of Rigid Particles in Contact. By
Professor Osborne Reynolds, M.A., F.R.S 989
9. On the Evidence deducible from the Study of Salts. By Spencer U.
Pickering 989
10 On the Molecular Weights of Solids and Salts in Solution. By Professor
W. A. TiLDEN, D.Sc, F.R.S 990
11. On the Moleculai Constitution of a Solution of Cobaltous Chloride. By
Professor W. J. Rtissell, Ph.D., F.R.S 991
WEDNESDAY, SEPTEMBER 16.
1. An Electrocentrifugal ^Machine for Laboratory use. By Alexander
Watt, F.I.C, F.C.S 991
2. Barium Sulphate as a Cementing Material in Sandstone. By Professor
Frank Clowes, D.Sc 992
3 An Apparatus for determining the Viscosity of Oils. By A. H. Allen,
F.C.S 992
4. The Action of Nitrous Gases upon Amyl Alcohol. Bv J. Williams,
F.C.S., F.I.C, and Mtles H. Smith, F.C.S .". 992
6. On the Action of Water on Lead. By A. II. Allen, F.C.S 993
Section C— GEOLOGY.
THURSDAY, SEPTEMBER 10.
Address by Professor J. W. Jtjdd, F.R.S., Sec.G.S., President of the Section 994
1. Report on the Volcanic Phenomena of Vesuvius 1013
2. Fifth Report on the Earthquake Phenomena of Japan 1013
3. On some recent Earthquakes on the Durham Coast, and their probable
cause. By Professor G. A. Lebotjr, M.A., F.G.S 1013
CONTENTS. IV
Page
4. Notice of an Outline Geological Map of Lower Egjpt, Arabia Petrsea,
and Palestine. By Professor Edward Hull, LL.D., F.R.S., F.G.S. ... 1015
5. On the Occurrence of Lower Old Red Conglomerate in the Promontory
of the Fanad, North Donegal. By Professor Edward Hull, LL.D.,
F.R.S., F.G.S 1016
6. On BastiteSerpentine and Troktolite in Aberdeenshire ; with a Note on
the Rock of the Black Dog. By Professor T. G. Bonnet, D.Sc, LL.D.,
F.R.S., Pres.G.S 1016
7. On certain Diatomaceous Deposits (Diatomite) from the Peat of Aber
deenshire. By W. Iyison Macadam, F.G.S., F.I.G 1017
8. List of Works on the Geology, Mineralogy, and Palaeontology of Stafford
shire, Worcestershire, and Warwickshire. Bv W. Whitaker, B.A.,
F.G.S., AssocInst.O.E '. 1017
FRIDAT, SEPTEMBER IL
1. The Volcanoes of Auvergne. By Tempest Anderson, M.D., B.Sc 1017
2. On the Rediscovery of lost Numidiaii Marbles in Algeria and Tunis.
By Lieut.Colonel R. L. Platfair 1018
3. Second Report on the Rate of Erosion of the Seacoasts of England and
Wales 1018
4. The Chasm called the Black Rock of Kiltearn. By William Watson 1018
5. The Bass of Inverurie, a fragment of an ancient Alluvial Bed. By the
Rev. John Davidson, D.D 1018
6. Thirteenth Report on the Erratic Blocks of England, Wales, and Ireland 1019
7. The Direction of Glaci;ition as ascertained by the Form of the Striae.
By Professor H. Carvill Lewis 1019
8. Proposed Conditions to account for a former Glacial Period in Great
Britain, existing under similar meteorological conditions to those that
rule at the present time. By W. F. Stanley, F.G.S., F.R.M.S 1020
9. On the Fyunon Beuno and Cae Gwyn BoneCaves, North Wales. By
H. Hicks, M.D., F.R.S., F.G.S 1021
10. Note on Specimens of Fish from the Lower Old Red Sandstone of For
farshire. By the Rev. Hugh Mitchell 1023
SATURDAY, SEPTEMBER 12.
1. The Elgin Sandstones. By J. Gordon Phillips 1023
2. Preliminary Note on a new Fossil Reptile recently discovered at New
Spy nie, near Elgin. By Dr. R. H. Tkaquaik, F.R.S 1024
3. Report on the Fossil Plants of tbe Tertiary and Secondary Beds of the
United Kingdom 1025
MONDAY, SEPTEMBER 14.
1. The Highland Controversy in British Geology: its Causes, Course, and
Consequences. By Professor Charles Lapworth, LL.D., F.G.S 1025
2. The Geology of Durness and Eriboll, with special reference to the High
land Controversy. By B. N. Peach, F.R.S.E., and J. Horne, F.R.S. E. 1027
3. Preliminary Note on some Traverses of the Crystalline District of the
Central Alps. By Professor T. G. Bonnet, D.Sc, LL.D., F.R.S.,
Pres. G.S 1027
xvi CONTENTS.
Page
4. Some Examples of PressureFluxion in Pennsylvania. By Professor
H. Cakvlll Lewis 1029
5. On Slaty Cleavage and allied Rock Structures, with special reference to
the Mechanical Theories of their Origin. By Alfred Haeker, M.A.,
F.G.S 1030
6. On Irish Metamorphic Rocks. By G. Henry Kinahan, M.R.I.A lOSO'
7. On Rocks of Central Caithness. By John^ Gtjnn 1030
8. On some Rock Specimens from the Islands of the Fernando Noronha
Group. By Professor A. Renabd, LL.D., F.G.S 1031
9. On the Average Density of Meteorites compared with that of the Earth.
By the Rev. E. Hill, M.A., F.G.S 1031
TUESDAY, SEPTEMBER 15.
1. Notes on a recent Examination of the Geology of East Central Africa.
By Professor Henrt Drummond, F.R.S.E., F.G.S 1032'
2. Report on the Rocks collected by H. "W. Johnston, Esq., from the upper
part of the Kilimanjaro Massiif. By Professor T. G. Boxnet, D.Sc,
LL.D., F.R.S., Pres.G.S 1032
3. Some Results of the CrystaUographic Study of Danburite. By Max
Schuster '. 1033
4. American Evidences of Eocene Mammals of the ' Plastic Clay ' Period.
By Sir Richard Owex, K.0.B.,F.R.S., F.G.S 1033
5. Discovery of Anurous Amphibia in the Jurassic Deposits of America.
By Professor 0. C. Marsh 1033
6. Third Report on the Fossil Phyllopoda of the Palaeozoic Rocks 1033
7. On the Distribution of Fossil Fishes in the Estuariue Beds of the
Carboniferous Formation. By Dr. Traquair 1033
8. Some Results of a detailed Sur^ey of the Old Coastlines near Trondh
jem, Norway. By Hugh Miller, F.G.S 1033
9. The Parallel Roads of Lochaber. By James Melvin 1035
10. Further Evidence of the Extension of the Ice in the North Sea during the
Glacial Period. By B. N. Peach, F.R.S.E., and J. Horne, F.R.S.E.... 103(>
11. Recent Advances in West Lothian Geology. By H. M. Cadell, B.Sc. 1037
12. Barium Sulphate as a Cementing Material in Sandstone. By Professor
Frank Clowes, D.Sc ". 1038
13. Notes on Fuller's Earth and its applications. By A. C. G. Cameron ... 1039
WEDNESDAY, SEPTEMBER 16.
1. On the Glacial Deposits at Montrose. By Dr. Howden 1040
2. Notes on the Rocks of St. Kilda. By Alexander Ross, F.G.S 1040
3. Eleventh Report on the Circulation of Underground Waters in the Per
meable Formations of England and AVales, and the Quantity and
Character of the Water supplied to various Towns and Districts from
these Formations 1041
4. On Deep Borings at Chatham : a Contribution to the Deepseated Geology
of the London Basin. By W. Whitaker,B.A., F.G.S., Assoc. Inst.C.E. 1041
5. On the Waterworks at Goldstone Road, Brighton. By W. Whitaker,
B.A., F.G.S., Assoc.Inst.C.E " 1041
CONTENTS. XVll
Section D.— BIOLOGY.
THURSDAY, SEPTEMBER 10.
Page
Address by Professor W. 0. McIntosh, M.D., LL.D., F.R.S. L. & E., F.L.S.,
President of the Section 1043
1. On the Tay Whale {Megaptera longimana) and other Whales recently
ohtained in the district. By Professor Strtjthers, M.D., LL.D 1053
2. Is the Commissural Theory of the Corpus Callosum correct ? By Pro
fessor D. J. Hamilton, M.B 1054
3. The Evidence of Comparative Anatomy with regard to Localisation of
Function in the Cortex of the Brain. By Alex. Hill, M.A., M.B.,
M.R.O.S 1054
4. Report of the Committee for the Exploration of Kilimanjaro, and the
adj oining Mountains of Eastern Equatorial Africa 1055
5. Report of the Committee for arranging for the occupation of a Table at
the Zoological Station at Naples 1055
6. Report of the Committee for promoting the establishment of Marine
Biological Stations on the coast of the United Kingdom 1056
7. Report of the Committee for promoting the establishment of a Marine
Biological Station at Granton 1056
8. Report on recent Polyzoa 1056
9. Report on the Record of Zoological Literature 1056
10. Report on the Bibliography of certain Groups of Invertebrata 1056
FRIDAY, SEPTEMBER 11.
1. Recent Observations on the Habits and Instincts of Ants and Bees. By
Sir John Lubbock, Bart., F.R.S 1056
2. On the Carpal Bones in various Cetaceans. By Professor Strtjthers,
M.D., LL.D 1056
3. Account of the Dissection of the Rudimentary Hindlimb of Balcenoptera
musculm. By Professor Strtjthers, M.D., LL.D 1056
4. Some points in the Anatomy of Sowerby's Whale (Mesoplodon bidens).
By Professor W. Turner, M.B., F.R.S 1057
5. On the use of Graphic Representations of Life^histories in the teaching
of Botany. By Professor F. 0. Bower 1057
Supplementary Meeting. — Physiology.
1. On the Direct Action of Anaesthetics on the Frogheart. By J.
McGregorRobertson, M.A., M.B 1057
2. On the Action of Cold on Microphytes. By John G. McKendrick,
M.D., LL.D., F.R.S .' 1058
3. On the Action of Ozonised Air upon MicroOrganisms and Albumen in
Solution. By J. J. Coleman, F.C.S 1058
4. A new Theory of the Sense of Taste. By Professor J. Berry
Haycraft 1059
SATURDAY, SEPTEMBER 12.
1. On a Model of the Whale. By Captam Gray 1059
2, On the Hybridisation of Salmonidae at Howietoun. By Francis Day,
CLE 1059
1885. 0,
■xviii CONTENTS.
Page
3, On the Identification of the British Mosses by their Distinctive Cha
racters. B}^ Mrs. FAEatTHAESON, F.R.M.S 106?.
4. On the Flora of Caithness. By James F. Grant 1063
.5. On Chinese Insect White Wax. By A. Hosie 1064
6. On the Existence of Cephalopoda in the Deep Sea. By W. E. Hoyle... 1064
7. On the Echiuoderm Fauna of the Island of Ceylon. By Professor F.
Jeffrey Bell, M.A., Sec.R.M.S '. 1065
MONDAY, SEPTEMBER 14.
1. Report on the Aid given by the Dominion Government and the Govern
ment of the United States to the encouragement of Fisheries, and to the
investigation of the various forms of Marine Life on the coasts and
rivers of North America 1065
2. On the Size of the Brain in Extinct Animals. By Professor 0. C. Marsh 1065
3. On the Systematic Position of the Chamseleon, and its Affinities with
the Dinosauria. By Professor D'Aecy W. Thompson 1065
4. On the Hind Limb of Ichthyosaurus, and on the Morphology of Verte
brate Appendages. By Professor DArcy W. Thompson 1065
5 On the Origin of the Fishes of the Sea of Galilee. Bv Professor Edward
Hull, LL.D.,F.R.S ." 1066
Q, On the Cause of the Extreme Dissimilarity of the Faunas of the Red Sea
and Mediterranean. By Professor Edward Hull, LL.D., F.R.S 1068
7 On the Morphology of the Human Arterial System. Bv Professor
A. MacAlister, F.R.S " 1068
8. On the Viscera of Gymnotus electricus. By Professor Cleland, M.D.,
F.R.S 1068
9. On the Spiracle of Fishes in its relation to the Head, as developed in the
Higher Vertebrates. By Profe.«sor Cleland, M.D., F.R.S 1069
10. On the Tail of Myxine glutinosa. By Professor Cleland, M.D., F.R.S. 1069
11. On the Nucleus in the Frog's Ovum. By George Thin, M.D 1069
12. On the Structure and Arrangements of the St. Andrews Marine
Laboratory. By Professor McInxosh, M.D., LL.D., F.R.S 1071
13. Remarks on the work at the St. Andrews Marine Laboratory during
nine months. By Professor McIntosh, M.D., LL.D., F.R.S 1071
14 On the Chemical Composition of the Milk of the Porpoise. Bv Professor
PuRDiE, Ph.D., B.Sc '. 1072
15. On certain processes formed bv Oerapus on Tubulana indivisa. By
Professor McIntosh, M.D., LL.D., F.R.S .'. 1072
16. On a new British Staurocephalus. By Professor McIntosh, M.D., F.R.S. 1073
17. On certain remarkable Structures resembling Ova from Deep Water.
By Professor McIntosh, M.D., LL.D., F.R.S 1073
18. On the Ova of Callionymus lyra, L. (the Skulpin). By Professor
McIntosh, M.D., LL.D., F.R.S 1073
19. On the Zoocytium or Gelatinous Matrix of Ophrydium versatile. By
Professor Allen Haeker, F.L.S 1074
Supplementary Meeting. — Physiology.
1. On the Action of Atropine on the Secretion of the Kidney, its Evidence
as to the Mechanism of the Secretion. By J. McGregorRobertson,
M.A.,M.B 1075
CONTENTS. xix
Page
2. On a Chemical Difference between Living and Dead Protoplasm. By
Oscar Loew, Ph.D 1075
3. A Comparative View of the Albuminous Substances contained in the
Blood of Vertebrate and Invertebrate Animals. By W. D. Halli
BUETON, M.D., B.Sc, M.R.C.P 1077
4. On the Striated Muscles in the Gills of Fishes. By Dr. J. A.
McWiLLIAM 1077
5. On the Structme of the Intestine in the Hedgehog and the Mole. By
Dr. J. A. McWiLLiAM 1078
6. On PlantDigestion, especially as occurring in Carica papaya. By
Sidney MARim, M.D., B.Sc, M.E.C.P 1078
7. On a new kind of Colour Apparatus for Physiological Experiment. By
John Aiken 1079
8. On the Structure of Hyaline Cartilage. By Geoege Thin, M.D 1078
9. The Preservation and Prolongation of Life to 100 years. By Protheeoe
Smith, M.D 1079
SUPPLEMENTAET MEETING. — BOTANT.
1. On the Application of the Anatomical Method to the Determination
of the Materials of the Linnean and other Herbaria. By Professor
L. Radlkofer 1080
2. On the Influence of Impregnation on a Plant. By E. J, Lowe, F.R.S.... 1081
3. On the Impregnation of Composite Flowers. By E. J. Lowe, F.R.S. ... 1082
4. On the Occurrence of Fungi in the Roots of Orchids. By J. Macmillan 1083
5. Notes on Experiments as to the Formation of Starch in Plants under the
influence of the Electric Light. By H. Marshall Ward 1086
6. On the Flora of Banfishire. By the Rev. W. S. Bruce 1087
7. On the Flora of Elgin. By James Mackenzie 1087
8. On the Division and Conjugation of Spirogyra. By Dr. J. M. Macfar
LANE, F.R.S.E ". 1088
9. On a Microscopic Fungus in Fossil Wood, from Bowling. By Dr. J. M.
Macfarlane, F.R.S.E 1088
10. On a new Method of preparing the Epidermal Tissues of Pitcher Plants.
By Dr. J. M. Macfarlane, F.R.S.E 1088
11. On Aberdeenshire Plants as Food for Animals. By William Wilson,
jun 1088
TUESDAY, SEPTEMBEE 15.
1. Report on the Migration of Birds 1089
"2. Note on the Intelligence of the Dog. By Sir John Lttbbock, Bart., F.R.S. 1089
3. On the Development of the Foodfishes at the St. Andrews Marine
Laboratory. By Edward E. Prince 1091
4, On the Nest and Development of Gastrosteus gpinachia at the St. An
drews Marine Laboratory. By Edward E. Prince 1093
.5. On the Reproduction of the Common Mussel (Myttlus ediUis, L.) By
John Wilson IO94
6. On the Modification of the Trochal Disc of the Rotifera. By Professor
A. G. Bourne, D.Sc, F.L.S  IO95
a 2
XX CONTENTS.
Page
7. On Buddine in the OligocliEeta. By Professor A. G. Bofene, D.Sc,
F.L.S 109G
8. Demonstration of a new Moneron. By Professor D'Arcy W. Thompsoi^ 1097
9. On the Blastopore and MesoUast of Sabella. By Professor D'Arct W.
Thompson 1097
10. On the Annelids of the Genus Dero. By E. C. Botjsfield 1097
11. On some little known Freshwater Annelids. By E. C. Bousfield 1098
12. On the Coloration of the Anterior Segments in the Malanidse. By Pro
fessor Allen II.VKKER, F.L.S 1098
1.3. Systematique du genre Polygordius. By Julien Fraipont 1098
14. On some of our Migratory Birds, as first seen in Aberdeenshire. By
James Taylor 1098
Supplementary Meeting. — Anatomy.
1. On the Connection of the Os Odontoidium with the centrum of the axis
vertebra. By Professor D. J. Cunningham, F.R.S 1101
2. On the Curvature of the Spine in the Foetus and Child. By Dr. John
ston Symington 1101
3. On the Bronchial Syrinx of the Cuculidse and Caprimulgidse. By Frank
E. Beddard, M.A., F.R.S.E 1101
4. Contributions to the Structure of the Oligochseta. By Frank E. Bed
dard, M.A., F.R.S.E 110^
5. On the Cervical Vertebrae in Balaina mysticetus, &c. By Professor
Struthers, M.D., LL.D 1103
6. On the Development of the Foot of the Horse. By Professor Struthers,
M.D., LL.D '. llOa
7. On the Development of the Vertebraj of the Elephant. By Professor
Struthers, M.D., LL.D 110^
8. On the Kidneys of Gasteropoda and the Renal Duct of Paludina. By W.
B. Benham 1103
Section E.— GEOGRAPHY.
TIIUR.SDAY, SEPTEMBER 10.
1. The Indian Forest School. By Major F. Bailey, R.E., F.R.G.S 1104
2. Brazil. By Colin Mackenzie, F.R.G.S 1105
3. On the Progress of African Philology. By R. Needham Cust,
F.R.G.S '. ". 1105
4. On the Changes which have taken place in Tunis since the French Pro
tectorate. By Lieut.Colonel R. L. Playfaie 1105
FRIDAY, SEPTEMBER IL
Address by General J. T. Walker, C.B., R.E., LL.D., F.R.S., President of
the Section HOC?
1. The Indian Forest Survey. By Major F. Bailey, R.E., F.R.G.S 1121
2. Account of the Levelling Operations of the Great Trigonometrical Survey
of India. By Major A. W. Baied, R.E., F.R.S 112.3
3. Notes on the Physiography of Southern India. By Colonel B. R.
Bkanfill 1121
CONTENTS. XXI
Page
4. On a Trip from Upper Assam into the Kampti Country and the Western
Branch of the Irrawady River, made by Colonel R. B. AVoodthorpe,
R.E., and Major C. R. MacGregor. By Lieut.Colonel H. H. Qodwin
Adsten, F.R.S 1126
5. On the complete Exploration of Lake Yamdok in Tibet. By Tee
LAWNEX SaUNDEES 1126
<3. On Himalayan Snow Peaks. By Lieut.Colonel H. C. B. Taiinbr 1126
7. Notes on recent Mountaineering in the Himalaya. By Douglas AV.
Feeshfield, F.R.G.S 1127
MONDAY, SEPTEMBER 14.
1. Projected Restoration of the Reian Moeris, and the Province, Lake, and
Canals ascribed to the Patriarch Joseph. By Cope Whitehouse, M.A. 1127
2. Report of the Committee for furthering the Scientific Examination of the
Country in the vicinity of Mount Roraima in Guiana 1128
3. Mount Roraima. By Eveeard iii Thuen 1128
4. Report of the Committee appointed for the purpose of promoting the
Survey of Palestine 1128
5. The Cadastral Survey of India. By Lieut.Colonel W, Barron 1128
6. The Ordnance Survey of Cyprus. By Teelawney Saunders 1129
7. The Rivers of the Punjab. By General Robert Maclaqan,R.E 1129
8. On a Clinometer to use vdth a PlaneTable. By Major Hill 1131
9. On a supposed Periodicity of the Cyclones of the Indian Ocean, south of
the Equator 1131
10. The Portuguese Possessions in West Africa. By H. H. Johnston 1132
11. Northwest Australia, By J. G. Bartholomew 1132
TUESDAY, SEPTEMBER 15.
1. Antarctic Research. By Admiral Sir Erasmus OMMANNEr,C.B., F.R.S.,
F.R.G.S 1132
2. Geogiaphical Education. By J. Scott Kelxie 1133
3. On Overland Expeditions to the Arctic Coast of America. By John
Rae, M.D., LL.D., F.R.S., F.R.G.S 1133
4. On the best and safest Route by which to attain a High Northern
Latitude. By John Rae, M.D., LL.D., F.R.S., F.R.G.S 1136
5. Oceanic Islands and Shoals. By J. Y. Buchanan 1136
6. On the Depth of the permanently Frozen Stratum of Soil in British
North America. By General Sir J. Henet Lefeot, K.C.M.G., F.R.S. 1136
7. On Recent Explorations in New Guinea. By Coutts Teotter 1136
WEDNESDAY, SEPTEMBER 16.
1. On Journeyings in Southwestern China. By A. Hosie 1137
2. Notes on the large Southern Tributaries of the Rio Solimoes or Upper
Amazon in Brazil, with special reference to the Rio Jutahi. By Pro
fessor J. W. H. Teail 1138
3. The Depth and Temperature of some Scottish Lakes. By J. Y.
Buchanan 1138
XXll CONTENTS.
Page
4. On the Geographical Features of the Beauly Basin. By Tho. W.
Wallace ll;38
5. What has been done for the Geography of Scotland, and what remams
to he done. By H. A. Websteb 1138
6. On Bathyhypsographical Maps, with special reference to a Comhination
of the Ordnance and Admiralty Surveys. By E. G. Eavenstein,
F.K.G.S.. 1140
Section F.— ECONOMIC SCIENCE AND STATISTICS.
THURSDAY, SEPTEMBER 10.
1. Report of the Committee for continuing the inquiries relating to the
teaching of Science in Elementary Schools 1141
Address by Professor Henry Sidgwick, M.A., Litt.D., President of the
Section 1141
2. On the alleged Depression of Trade. By Professor Leone Levi, F.S.S... 11 ')5
3. On the Variations of PriceLevel since 1«50 By Michael G. IMulhall,
F.S.S 1157
FRIDAT, SEPT EM BE It 11.
1. On the Municipalisation of the Land. By Sir George Campbell,
K.CS.L, M.P 1158
2. The Agriculture of Aberdeenshire. By Colonel Innes 1161
3. The Agricultural Situation. By Professor W. Fream, B.Sc, F.L.S.,
F.G.S IIGI
4. On recent Changes in Scottish Agriculture. By Major P. G. Craigie.,. 11G2
SATURDAY, SEPTEMBER 12.
1. On the International Forestry Exhibition. By Dr. Ceombie Brown ... 1164
2. What is Capital ? By W. Westgarth 1165
3. On Methods of afcertainiug Variations in the Rates of Birth, Death, and
Marriage. By F. Y. Edgeworth 1165
4. On the Application of Biology to Economics. By Patrick Geddes IIGG
MONDAY, SEPTEMBER 14.
1. On the Use of Index Numbers in the Investigation of Trade Statistics.
By Stephen Bourne, F.S.S 1168
2. On Depression of Prices and Results of Economy of Production, and on
the Prospect of Recovery. By Hyde Clarke, F.S.S 1168
3. On Customs Tarifls. By A. E. Bateman 1160
4. How its Fiscal Policy may affect the Prosperity of a Nation. By
Alexander Forbes 11 60
3. On the Incidence of Imperial Taxation. By Dr. W. A. Hunter 1170
TUESDAY, SEPTEMBER 15.
1. State Guarantee of War Risks. By John Corry 1171
2. On the British Standard of Value. By Dana Horton 1172
CONTENTS. XXm
Page
3. Sliding Scales in the Coal Industry. By Professor J. E. C. Mttnro 1173
4. Anomalies in the condition of Scotch Miners in contrast with other un
skilled Labourers. By William Small 1174
6. The Statistics and some points in the Economics of the Scottish Fisheries.
By William Wati, F.S.S 1175
6. On the Pauperisation of Children by the Operation of the ' Scotch
Education Act, 1872.' By Matthew Blair 1176
WEDNESBAT, SEPTEMBER 16.
1. Agricultural Investigation and Education. By Thomas Jamieson 1177
2. Policy in Taxation. By J. B. Greig 1179
3. A new view of the Consequences of Unpunctuality in Railway Trains.
By Cornelius Walford, F.I.A., F.S.S 1180.
4. On the Industrial Remuneration Conference. By the Rev. W.
Cunningham, B.D 1181
Section G.— MECHANICAL SCIENCE.
THURSBAY, SEPTEMBER 10.
Address by B. Baker, M.Inst.C.E., President of the Section 1182
1. The New Tay Viaduct. By Crawford Barlow, B.A., M.Inst.C.E. ... 1192
2. The Forth Bridge Works. By Andrew S. Bjggart, C.E 1193
FRIBAY, SEPTEMBER 11.
1. The American System of Oil Pipe Lines. By J. H. Harris 1193
2. The Movement of Land in Aberdeen Bay. By W. Smith 1193
3. On Shallowdraught Screw Steamers for the Nile Expedition. By
J. T. Thornycroft, M.Inst.C.E 1193
4. The Sphere and Roller Friction Gear. By Professor H. S. Hele Shaw 1193
5. On the Employment of the Road Engine in Construction and Main
tenance of Roads. By Colonel Innes 1194
MOXBAY, SEPTEMBER 14.
1. Electric Lighting and the Law. By Dr. Leavis Edmunds 1195
2. On an Electric Safety Lamp for Miners. By J. Wilson Swan, M.A.... 1196
3. On the Strength of Telegraph Poles. By W. H. Preece, F.R.S.,
M.Inst.C.E 1197
4. On Domestic Electric Lighting. By W. H. Preece, F.R.S., M.Inst.C.E. 1197
5. On a System of Periodic Clock Control on Telephone or Telegraph Lines.
By Professor W. F. Barrett, F.R.S.E 1198
6. Electric Lighting at the Forth Bridge Works. By James N, Shool
bred, B.A., M.Inst.C.E 1198
7. On the Development of the Pneumatic System as applied to Telegraph
purposes. By J. W. Willmot 1198
TTTESBAY, SEPTEMBER 15.
1. Report of the Patent Law Committee 1199
2. Autographic Apparatus for Machines for Testing Materials. By Pro
fessor W. C. Unwin, M.Inst.C.E 1199
XXIV CONTENTS.
Page
3. Notes on Mild Steel. ByG.J. Goedon 1200
4. The Diminution of Casualties at Sea. By Don Artfko de Maecoakttj 1201
5. On the Deep Sea Channel into Swansea Harbour. By Robert Oappek 1202
6. On the Spey Bridge at Garmouth and the River Spey. By P. M.
Baenett 1203
7. On a New Form of High Speed Friction Driving Gear. By Professor
J. A. EwiNG ; 1203
8. On Ashton's New Power Meter. By Professor H. S. Hele Shaw 1203
9. On the British Association Standard Gauge for Small Screws. By
Edwaed Rigg, M.A 1203
Section H.— ANTHROPOLOGY.
THURSDAY, SEPTEMBER 10.
1. The Scope of Anthropology, and its relation to the Science of Mind.
By Alexander Bain, LL.D 1204
2. The Index of the Pelvic Brim as a Basis of Classification. By Professor
W. TuENER, M.B., F.R.S 1205
3. A Portable Scale of Proportions of the Human Body. By W. F.
Stanley, F.G.S., F.K.M.S 1206
Address by Francis Galton, M.A., F.R.S., President of the Anthropo
logical Institute, President of the Section 1206
FRIDAY, SEPTEMBER 11.
1. Insular Greek Customs. By J. Theodore Bent 1214
2. On the Working of the Ancient Monuments Act of 1882. By General
PiTTRivERs, r.R.S 1214
3. American Shellwork and its Affinities. By Miss A. W. Buckland ...1214
4. Note on the Redmen about Roraima. By E. F. im Thtten 1215
5. A Game with a History. By J. W. Crombie, M.A 1215
6. The Rule of the Road from an Anthropological point of view. By Sir
George Campbell, K.O.S.I 1215
7. On the Modes of Grinding and Drying Corn in old times. By Miss Jeanie
M. Laing 1216
8. The Flintknappers' Art in Albania. By A. J. Evans 1216
9. The Discovery of Naukiatis. By W. M. Flinders Petrie 1216
MONDAY, SEPTEMBER 4.
1. On Ancient Tombs in the Greek Islands. By J. Theodore Bent 1217
2. A New Cave Man of Mentone. By Thomas Wilson 1218
3. Happaway Cavern, Torquay. By William Pengellt, F.R.S., F.G.S. , 1219
4. On the Human Remains found in Happaway Cavern, Torquav. By
J. G. gaeson, m.d :. ....•; ;; 1220
5. On Three Stone Circles in Cumberland, with some further observations
on the relation of Stone Circles to adjacent hills and outlying stones.
By A. L. Lewis, M.A.I ...Tf. 1220
CONTENTS. XXV
Page
6. The Archaeological Importance of ancient British Lakedwellings and
their relation to analogous remains in Europe. By R. Munko,
M.A., M.D 1221
7. The Stone Circles in Aherdeenshire, with special reference to those in
the more Lowland parts of the County, their Extent and Arrangement,
singly or in gioups, with General Observations. By the Rev. James
Peter, F.S.A.Scot '. 1221
8. Stone Circles in Aberdeenshire. By John Mtlne, M.A 1223
9. Notes on a recent Antiquarian Find in Aberdeenshire. By Dr. F. Mait
LAND MoiB 1223
10. The Picts and PrjeCeltic Britain. By Hyde Clarke 1223
11. Report of the Committee for investigating and publishing reports on
the physical characters, languages, and industrial and social condi
tions of the Northwestern Tribes of the Dominion of Canada 1224
TUESDAY, SEPTEMBER 15.
1. Notes on the opening of a Cist in the parish of Leslie, Aberdeenshire.
By the Rev. John Russeu, M.A 1224
2. Notes on a Cist found at Parkhill, Dyce, in October 1881. By W.
Ferguson 1225
3. On the Human Crania and other contents found in short stone Cists in
Aberdeenshire. By Professor J. Struthers, M.D., LL.D 1225
4. Notice of Human Bones found in 1884 in Balta Island, Shetland, by
D. Edmonston, Esq. By Professor J. Struthers, M.D., LL.D 1225
6. Some Important Points of Comparison between the Chimpanzee and
Man. By Professor D. J. Cunningham 1226
6. Abnormal and Arrested Development as an Indication of Evolutionary
History. By J. G. Garson, M.D 1226
7. The Symbol Pillars abounding in Central Aberdeenshire. Bv the Rev.
John Davidson, D.D .* 1227
8. Notes on some of the Bantu Tribes living round Lake Nyasa in Eastern
Central Africa. By Dr. Robert Laws 1227
9. Exhibition of the Skeleton of a Strandlouper from South Africa. By
Professor A. Macalister, F.R.S 1228
10. A brief Account of the Nicobar Islanders, with .special reference to the
Inland Tribe of Great Nicobar. By E. H. Man 1228
11. A proposed Society for Experimental Psychology. By Joseph Jacobs,
B.A : 1230
12. A Comparative Estimate of Jewish Ability. By Joseph Jacobs, B.A.... 1231
13. Traces of Early Human Habitations on Deeside and Vicinity. By the
Rev. J. G. Michie, A.M 1232
Index 1233
XXVI LIST OF PLATES.
LIST OF PLATES.
PLATES I., IL, AND III.
Illustrating the Eeport of the Committee on the Fossil Plants of tlie Tertiary andl
Secondary Beds of the United Kingdom.
PLATE IV.
Illustrating the Report ot the Committee on the Erosion of the Seacoasts of
England and Wales.
PLATES V. AND Va.
Illustrating Mr. Meldrum's Communication, ' A Tabular Statement of the Dates
at which, and the Localities where. Pumice or Volcanic Dust was seen in the
Indian Ocean in 188384.'
PLATE VI.
Illustrating Mr. Andrew S. Biggart's Communication, ' The Forth Bridge Works.'
PLATE VII.
Illustrating Mr. Crawford Barlow's Communication, ' The New Tay Viaduct.'
OBJECTS AND RULES
OF
THE ASSOCIATION.
OBJECTS.
The Association contemplates no interference with the ground occupiedl
by other institutions. Its objects are : — To give a stronger impulse and
a more systematic direction to scientific inquiry, — to promote the inter
course of those who cultivate Science in different parts of the British
Empire, with one another and with foreign philosophers, — to obtain a
more general attention to the objects of Science, and a removal of any
disadvantages of a public kind which impede its progress.
RULES.
Admission of Members and Associates.
All persons who have attended the first Meeting shall be entitled to
become Members of the Association, upon subscribing an obligation to
conform to its Rules.
The Fellows and Members of Chartered Literary and Philosophical
Societies publishing Transactions, in the British Empire, shall be entitled,,
in like manner, to become Members of the Association.
The Officers and Members of the Councils, or Managing Committees,
of Philosophical Institutions shall be entitled, in like manner, to become
Members of the Association.
All Members of a Philosophical Institution recommended by its Coun
cil or Managing Committee shall be entitled, in like manner, to become
Members of the Association.
Persons not belonging to such Institutions shall be elected by the
General Committee or Council, to become Life Members of the Associa
tion, Annual Subscribers, or Associates for the year, subject to the
approval of a General Meeting.
Compositions, Subscriptions, and Privileges.
Life Members shall pay, on admission, the sum of Ten Pounds. They
shall receive gratuitously the Reports of the Association which may be
published after the date of such payment. They are eligible to all the
offices of the Association.
Annual Subscribers shall pay, on admission, the sum of Two Pounds,
and in each following year the sum of One Pound. They shall receive
gratuitously the Reports of the Association for the year of their admission
and for the years in which they continue to pay without intermission their
Annual Subscription. By omitting to pay this subscription in any par
ticular year, Members of this class (Annual Subscribers) Insp for that and
iXVlU RULES OF THE ASSOCIATION.
all future years tlie privilege of receiving the volumes of the Association
gratis : but they may resume their Membership and other privileges at
any subsequent Meeting of the Association, paying on each such occasion
the sum of One Pound. They are eligible to all the Offices of the Asso
•ciation.
Associates for the year shall pay on admission the sum of One Pound.
They shall not receive gratuitously the Reports of the Association, nor be
eligible to serve on Committees, or to hold any office.
The Association consists of the following classes : —
1. Life Members admitted from 1831 to 1845 inclusive, who have paid
on admission Five Pounds as a composition.
2. Life Members who in 1846, or in subsequent years, have paid on
admission Ten Pounds as a composition.
3. Annual Members admitted from 1831 to 1839 inclusive, subject to
the payment of One Pound annually. [May resume their Membership
after intermission of Annual Payment.]
4. Annual Members admitted in any year since 1839, subject to the
payment of Two Pounds for the first year, and One Pound in each
ifollowing year. [May resume their Membership after intermission of
Annual Payment.]
5. Associates for the year, subject to the payment of One Pound.
6. Corresponding Members nominated by the Council.
And the Members and Associates will be entitled to receive the annual
volume of Reports, gratis, or to 2^^^'''<^^>(^^^ it at reduced (or Members')
•price, according to the following specification, viz. : —
1. Gratis. — Old Life Members who have paid Five Pounds as a com
position for Annual Payments, and previous to 1845 a fur
ther sum of Two Pounds as a Book Subscription, or, since
1845, a further sum of Five Pounds,
New Life Members who have paid Ten Pounds as a compo
sition.
Annual Members who have not intermitted their Annual Sub
scription.
2. At reduced or Memhers" Prices, viz. twothirds of the Publi
cation Price. — Old Life Members who have paid Five Pounds
as a composition for Annual Payments, but no further sum
as a Book Subscription.
Annual Members who have intermitted their Annual Sub
scription.
Associates for the year. [Privilege confined to the volume
for that year only.]
3. Members may purchase (for the purpose of completing their sets)
any of the volumes of the Reports of the Association up
to 1874, of lohich more than 15 copies remain, at 2s. 6c?. per
volume. •
Application to be made at the Office of the Association, 22 Albemarle
Stieet, London, W.
Volumes not claimed within two years of the date of publication can
•only be issued by direction of the Council.
Subscriptions shall be received by the Treasurer or Secretaries.
' A few complete sets, 1831 to 1874, are on sale, £10 the set.
RULES OF THE ASSOCIATION. XXIX
Meetings.
The Association shall meet annually, for one week, or longer. The
place of each Meeting shall be appointed bj^ the General Committee two
years in advance ; and the arrangements for it shall be entrusted to the
Officers of the Association.
General Committee.
The General Committee shall sit during the week of the Meeting, or
longer, to transact the business of the Association. It shall consist of the
following persons : —
Class A. Peejiaxent Members.
1. Members of the Council, Presidents of the Association, and Presi
dents of Sections for the present and preceding years, with Authors of
Reports in the Transactions of the Association.
2. Members who by the publication of Works or Papers have fur
thered the advancement of those subjects which are taken into consideia
tion at the Sectional Meetings of the Association. With a view of sub
mitting neio claims under this Rule to the decision of the Council, they must
be sent to the Secretary at least one month before the Meeting of the
Association. The decision of the Council on the claims of any Member of
the Association to be placed on the list of the General Committee to be final.
Class B. Temporary Members.'
1. Delegates nominated by the Corresponding Societies under the
conditions hereinafter explained. Claims under this Rule to be sent to the
Secretary before the opening of the Meeting.
2. Officebearers for the time being, or delegates, altogether not ex
ceeding three, from Scientific Institutions established in the place of
Meeting. Claims under this Rule to be approved by the Local Secretaries
before the opening of the Meeting.
3. Foreigners and other individuals whose assistance is desired, and
who are specially nominated in writing, for the Meeting of the year, by
the President and General Secretaries.
4. VicePresidents and Secretaries of Sections.
Organizing Sectional Committees.^
The Presidents, VicePresidents, and Secretaries of the several Sec
tions are nominated by the Council, and have power to act until their
names are submitted to the General Committee for election.
From the time of their nomination they constitute Organizing Com
mittees for the purpose of obtaining information upon the Memoirs and
Reports likely to be submitted to the Sections,^ and of preparing Reports
thereon, and on the order in which it is desirable that they should be
read, to be presented to the Committees of the Sections at their first
' Revised by the General Committee, 188i.
 Passed by the General Committee, Edinburgh, 1871.
' Kofict' to Contribtitois of Memoirs. — Authors are reminded that, under an
arrangement dating from 1871, the acceptance of Memoirs, and tlie days on which
they are to be read, are now as far as possible determined by Organizing Committees
for the several Sections before the hef/inninr/ of the Meeting. It has therefore become
necessary, in order to give an opportunity to the Committees of doing justice to the
several Communications, that each Author should prepare an Abstraci'of his Memoir,
of a length suitable for insertion in tJie published Transactions of the Association,
and that he should send it, together with the original Memoir, by bookpost, on or
XXX RULES OF THE ASSOCIATION.
meeting. The Sectional Presidents of former years are ex ojjicio members
of the Organizing Sectional Committees.'
An Organizing Committee may also hold such preliminary meetings as
the President of the Committee thinks expedient, but shall, under any
circumstances, meet on the first Wednesday of the Annual Meeting, at
11 A.M., to nominate the first members of the Sectional Committee, if
they shall consider it expedient to do so, and to settle the terms of their
report to the General Committee, after which their functions as an
Organizing Committee shall cease. ^
Constitution of the Sectional Comviittees.^
On the first day of the Annual Meeting, the President, VicePresi
dents, and Secretaries of each Section having been appointed by the
General Committee, these Officers, and those previous Presidents and
VicePresidents of the Section who may desire to attend, are to meet, at
2 P.M., in their Committee Rooms, and enlarge the Sectional Committees
by selecting individuals from among the Members (not Associates) present
at the Meeting whose assistance they may particularly desire. The Sec
tional Committees thus constituted shall have power to add to their
number from day to day.
The List thus formed is to be entered daily in the Sectional Minute
Book, and a copy forwarded without delay to the Printei, who is charged
with publishing the same before 8 A.M. on the next day in the Journal of
the Sectional Proceedings.
Business of the Sectional Comviittees.
Committee Meetings are to be held on the Wednesday at 2 p.m., on the
following Thursday, Friday, Saturday,^ Monday, and Tuesday, from 10 to
11 A.M., punctually, for the objects stated in the Rules of the Association,
and specified below.
The business is to be conducted in the following manner : —
1. The President shall call on the Secretary to read the minutes of
the previous Meeting of the Committee.
2. No paper shall be read until it has been formally accepted by the
Committee of the Section, and entered on the minutes accord
ingly.
3. Papers which have been reported on unfavourably by the Organiz
ing Committees shall not be brought before the Sectional
Committees.®
At the first meeting, one of the Secretaries will read the Minutes of
last year's proceedings, as recorded in the MinuteBook, and the Synopsis
before , addressed thus — 'General Secretaries, British Associa
tion, 22 Albemarle Street, London, W. For Section ' If it should be incon
venient to the Author that his paper should be read on any particular days, he is
requested to send information thereof to the Secretaries in a separate note. Authors
who send in their MSS. three complete weeks before the Meeting, and whose papers
are accepted, will be furnished, before the Meeting, with printed copies of their
Eeports and Abstracts. No Report, Paper, or Abstract can be inserted in the Annual
Volume unless it is handed either to the Recorder of the Section or to the Secretary,
■be/ore the conclusion of the Mcetin/f.
' Added by the General Committee, Sheffield, 1879.
2 Revised by the General Committee, Swansea, 1880.
' Passed by the General Committee, Edinburgh, 1871.
* The meeting on Saturday was made optional by the General Committee at
Pouthport, 1883.
' These rules were adopted by the General Committee, Plymouth, 1877.
KOLES OF THE ASSOCIATION. XXXI
of Recommendatious adopted at the last Meeting of the Association and
printed in the last volume of the Transactions. He will next proceed to
read the Report of the Organizing Committee.' The list of Communi
cations to be read on Thursday shall be then arranged, and the general
distribution of business throughout the week shall be provisionally ap
pointed. At the close of the Committee Meeting the Secretaries shall
forward to the Printer a List of the Papers appointed to be read. The
Printer is charged vidth publishing the same before 8 A.M. on Thursday in
the Journal.
On the second day of the Annual Meeting, and the follovring days,
the Secretaries are to correct, on a copy of the Jouinal, the list of papers
which have been read on that day, to add to it a list of those appointed
to be read on the next day, and to send this copy of the Journal as early
in the day as possible to the Printer, who is charged with printing the
same before 8 a.m. next morning in the Journal. It is necessary that one
of the Secretaries of each Section (generally the Recorder) should call
at the Printing Office and revise the proof each evening.
Minutes of the proceedings of every Committee are to be entered daily
in the MinuteBook, which should be confirmed at the next meeting of
the Committee.
Lists of the Reports and Memoirs read in the Sections are to be entered
in the ^linuteBook daily, which, with all Memoirs and Copies 07 Abstracts
of Memoirs furnished hy Autlwrs, are to hefonvarded, at the close of the Sec
tional Meetings, to the Secretary.
The VicePresidents and Secretaries of Sections become ex officio tem
porary Members of the General Committee (vide'p. xxix), and will receive
on application to the Treasurer in the Reception Room, Tickets entitling
them to attend its Meetings.
The Committees will take into consideration any suggestions which may
be offered by their Members for the advancement of Science. They are
specially requested to review the recommendations adopted at preceding
Meetings, as published in the volumes of the Association and the com
munications made to the Sections at this Meeting, for the purposes of
selecting definite points of research to which individual or combined
exertion may be usefully directed, and branches of knowledge on the state
and progress of which Reports are wanted ; to name individuals or Com
mittees for the execution of such Reports or researches ; and to state
whether, and to what degree, these objects may be usefully advanced by
+he appropriation of the funds of the Association, by application to
Government, Philosophical Institutions, or Local Authorities.
In case of appointment of Committees for special objects of Science
it is expedient that all Members of the Committee shovld be named and
one of them appointed to act as Secretary, for insuring attention to business.
Committees have power to add to their number persons whose assist
ance they may require.
The recommendations adopted by the Committees of Sections are to
be registered in the Forms furnished to their Secretaries, and one Copy of
each is to be forwarded, without delay, to the Secretary for presentation
to the Committee of Recommendations. Unless this be done, the Eecom
mendations cannot receive the sanction of the Association.
N.B. — Recommendations which may originate in any one of the Sec
tions must first be sanctioned by the Committee of that Section before they
' This and the following sentence were added by the General Committee 1871.
xxxii KULES OF THE ASSOCIATION.
can be referred to the Committee of Recommendations or confirmed by
the General Committee.
The Committees of the Sections shall ascertain whether a Report has
been made by every Committee appointed at the previous Meeting to whom
a sum of money has been granted, and shall report to the Committee of
Recommendations in every case where no such Report has been received.'
Notices regarding Ghxmts of Money.
Committees and individuals, to whom grants of money have been
entrusted by the Association for the prosecution of particular researches
in science, are required to present to each following Meeting of the
Association a Report of the progress which has been made ; and the
Individual or the Member first named of a Committee to whom a money
grant has been made must (previously to the next Meeting of the Associa
tion) forward to the General Secretaries or Treasurer a statement of the
sums which have been expended, and the balance which remains dispos
able on each grant.
Grants of money sanctioned at any one Meeting of the Association
expire a lueek before the opening of the ensuing Meeting: nor is the
Treasurer authorized, after that date, to allow any claims on account of
such grants, unless they be renewed in the original or a modified form by
the General Committee.
No Committee shall raise money in the name or under the auspices of
the British Association without special permission from the General Com
mittee to do so ; and no money so raised shall be expended except in
accordance with the rules of the Association.
In each Committee, the Member first named is the only person entitled
to call on the Treasurer, Professor A. W. Williamson, University College,
London, W.C, for such portion of the sums granted as may from time to
time be required.
In grants of money to Committees, the Association does not contem
plate the payment of personal expenses to the members.
In all cases where additional grants of money are made for the con
tinuation of Researches at the cost of the Association, the sum named is
deemed to include, as a part of the amount, whatever balance may remain
unpaid on the former grant for the same object.
All Instruments, Papeis, Drawings, and other property of the Associa
tion are to be deposited at the OfiBlce of the Association, 22 Albemarle
Street, Piccadilly, London, W., when not employed in carrying on scien
tific inquiries for the Association.
Business of the Sections.
The Meeting Room of each Section is opened for conversation from
10 to 11 daily. The Section Booms and approaches thereto can he used for
no notices, exhibitions, or other purposes than those of the Association.
At 11 precisely the Chair will be taken, ^ and the reading of communi
cations, in the order previously made public, commenced. At 3 p.m. the
Sections will close.
Sections may, by the desire of the Committees, divide them.3elves into
Departments, as often as the number and nature of the communications
delivered in may render such divisions desirable.
' Passed by the General Committee at Sheffield, 1879.
 The meeting on Saturday may begin, if desired by the Committee, at any time not
earlier than 10 or later than 11. Passed by the General Committee at Southport, 188.3.
RULES OF THE ASSOCIATION. XXXm
A Report presented to the Association, and read to the Section which
originally called for it, may be read in another Section, at the request of
the Officers of that Section, with the consent of the Author.
Duties of the Doorkeepers.
1. — To remain constantly at the Doors of the Rooms to which they are
appointed during the whole time for which they are engaged.
2. — To require of every person desirous of entering the Rooms the ex
hibition of a Member's, Associate's, or Lady's Ticket, or Reporter's
Ticket, signed by the Treasurer, or a Special Ticket signed by the
Secretary.
3. — Persons unprovided with any of these Tickets can only be admitted
to any particular Room by order of the Secretary in that Room.
No person is exempt from these Rules, except those Officers of the
Association whose names are printed in the programme, p. 1.
Duties of the Messengers.
To remain constantly at the Rooms to which they are appointed dar
ing the whole time for which they are engaged, except when employed on
messages by one of the Officers directing these Rooms.
Committee of Recommendations.
The General Committee shall appoint at each Meeting a Committee,
which shall receive and consider the Recommendations of the Sectional
Committees, and report to the Geneml Committee the measures which
they would advise to be adopted for the advancement of Science.
All Recommendations of Grants of Money, Requests for Special Re
searches, and Reports on Scientific Subjects shall be submitted to the
Committee of Recommendations, and not taken into consideration by the
General Committee unless previously recommended by the Committee of
Recommendations.
Ooo'responding Societies.^
(1.) Any Society is eligible to be placed on the List of Corresponding
Societies of the Association which undertakes local scientific investiga
tions, and publishes notices of the results.
(2.) Applications may be made by any Society to be placed on the
List of Corresponding Societies. Application must be addressed to the
Secretary on or before the 1st of June preceding the Annual Meeting at
which it is intended they should be considered, and must be accompanied
by specimens of the publications of the results of the local scientific
investigations recently undertaken by the Society.
(3.) A Corresponding Societies Committee shall be annually nomi
nated by the Council and appointed by the General Committee for the
purpose of considering these applications, as well as for that of keeping
themselves generally informed of the annual work of the Corresponding
Societies, and of superintending the preparation of a list of the papers
published by them. This Committee shall make an annual report to the
General Committee, and shall suggest such additions or changes in the
List of Corresponding Societies as they may think desirable.
(4.) Every Corresponding Society shall return each year, on or
before the 1st of June, to the Secretary of the Association, a schedule,
' Pas.serl by the General Committee, 1884.
1885. b
XXXiv RULES OP THE ASSOCIATION.
properly filled np, which will be issued by the Secretary of the Associa
tion, and which will contain a request for such particulars with regard to
the Society as may be required for the information of the Corresponding
Societies Committee.
(5.) There shall be inserted in the Annual Report of the Association
a list, in an abbreviated form, of the papers published by the Corre
sponding Societies during the past twelve months which contain the
results of the local scientific work conducted by them ; those papers only
Taeing included which refer to subjects coming under the cognizance of
one or other of the various Sections of the Association.
(0.) A Corresponding Society shall have the right to nominate any
one of its members, who is also a Member of the Association, as its dele
gate to the Annual Meeting of the Association, who shall be for the time
a Member of the General Committee.
Conference of Delegates of Corresponding Societies.
(7.) The Delegates of the various Corresponding Societies shall con
stitute a Conference, of which the Chairman, Vice Chairmen, and Secre
taries shall be annually nominated by the Council, and appointed by the
General Committee, and of which the members of the Coiresponding
Societies Committee shall be ex officio members.
(8.) The Conference of Delegates shall be summoned by the Secretaries
to hold one or more meetings during each Annual Meeting of the Associa
tion, and shall be empowered to invite any Member or Associate to take
part in the meetings.
(9.) The Secretaries of each Section shall be instructed to transmit to
the Secretaries of the Conference of Delegates copies of any recommenda
tions forwarded by the Presidents of Sections to the Committee of Re
commendations bearing upon matters in which the cooperation of
Corresponding Societies is desired ; and the Secretaries of the Conference
of Delegates shall invite the authors of these recommendations to attend
the meetings of the Conference and give verbal explanations of their
objects and of the precise way in which they would desire to have them
carried into efiect.
(10.) It will be the duty of the Delegates to make themselves familiar
with the purport of the several recommendations brought before the Confer
ence, in order that they and others who take part in the meetings may be
able to bring those recommendations clearly and favourably before their
respective Societies!. The Conference may also discuss propositions bear
ing on the promotion of more systematic observation and plans of opera
tion, and of greater uniformity in the mode of publishing I'esults.
Local Cornmittees.
Local Committees shall be formed by the Officers of the Association
to assist in making arrangements for the Meetings.
Local Committees shall have the power of adding to their numbers
those Members of the Association whose assistance they may desire.
Officers.
A President, two or more VicePresidents, one or more Secretaries,
and a Treasurer shall be annually appointed by the General Committee.
RULES OF THE ASSOCIATION. XXXV
Council.
In the intervals of the Meetings, the affairs of the Association shall
be managed by a Conncil appointed by the General Committee. The
Council may also assemble for the despatch of business during the week
of the Meeting.
Papers and Communications.
The Author of any paper or communication shall be at liberty to
reserve his right of property therein.
Accounts.
The Accounts of the Association shall be audited annually, by Auditors
appointed by the General Committee.
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PRESIDENTS AND SECRETARIES OF THE SECTIONS.
xliii
Presidents and Secretaries of the Sections of the Association.
Date and Place
Presidents
Secretaries
MATHEMATICAL AND PHYSICAL SCIENCES.
COMMITTEE OF SCIENCES, I. — MATHEMATICS AND GENERAL PHYSICS.
1832. Oxford
1833. Cambridge
Davies Gilbert, D.C.L., F.E.S.
Sir D. Brewster, F.R.S.
1834. Edinburgh Rev. W. ^Vhewell, F.R.S.
Rev. H. Coddington.
Prof. Forbes.
Prof. Forbes, Prof. Lloyd.
1835. Dublin
1836. Bristol
1837. Liverpool...
1838. Newcastle
1839. Birmingham
1840. Glasgow ...
1841. Plymouth
1842. Manchester
SECTION A. — MATHEMATICS AND PHYSICS.
Rev. Dr. Robinson
1843. Cork
1844. York
1845. Cambridge
1846. Southamp
ton.
1847. Oxford
1848. Swansea ...
1849. Birmingham
1850. Edinburgh
1851. Ipswich ...
1852. Belfast
1853. Hull
1854. Liverpool...
1855. Glasgow ...
1856. Cheltenham
1857. Dublin
1858. Leeds
Rev. William WTiewell, F.R.S.
Sir D. Brewster, F.R.S
Sir J. F. W. Herschel, Bart.,
F.R.S.
Rev. Prof . Whewell, F.R.S....
Prof. Forbes, F.R.S
Rev. Prof. Lloyd, F.R.S
Very Rev. G. Peacock, D.D.,
F R S
Prof. M'Culloch, M.R.I. A. ...
The Earl of Rosse, F.R.S. ...
The Very Rev. the Dean of
Ely.
Sir John F. W. Herschel,
Bart., F.R.S.
Rev. Prof. Powell, M.A.,
F.R.S.
Lord Wrottesley, F.R.S
William Hopkins, F.R.S
Prof. J. D. Forbes, F.E.S.,
Sec. R.S.E.
Rev. W. Whewell, D.D.,
F.R.S.
Prof. W. Thomson, M.A.,
F.R.S. L. & E.
The Verj' Rev. the Dean of
Ely, F.R.S.
Prof. G. G. Stokes, M.A., Sec.
E.S.
Rev. Prof. Kelland, M.A.,
F.R.S. L. & E.
Rev. R. Walker, M.A., F.R.S.
Rev. T. R. Robinson, D.D.,
F.R.S., M.R.I.A.
Rev. W. Whewell, D.D.,
V.P.R.S.
Prof. Sir W. R. Hamilton, Prof.
Wheatstone.
Prof. Forbes, W. S. Harris, F. W.
Jerrard.
W. S. Harris, Rev. Prof. Powell,
Prof. Stevelly.
Rev. Prof. Chevallier, Major Sabine,
Prof. Stevelly.
J. D. Chance, W. Snow Harris, Prof.
Stevelly.
Rev. Dr. Forbes, Prof. Stevelly,
Arch. Smith.
Prof. Stevelly.
Prof. M'Cuhoch, Prof. Stevelly, Rev.
W. Scoresby.
J. Nott, Prof .■ Stevelly.
Rev. Wm. Hey, Prof. Stevelly.
Rev. H. Goodwin, Prof. Stevelly,
G. 6. Stokes.
John Drew, Dr. Stevelly, G. G.
Stokes.
Rev. H. Price, Prof. Stevelly, G. G.
Stokes.
Dr. Stevelly, G. G. Stokes.
Prof. Stevelly, G. G. Stokes, W.
Eidout Wills.
W. J.Macquorn Rankine, Prof .Smyth,
Prof. Stevelly, Prof. G. G. Stokes.
S. Jackson, W. J. Macquorn Rankine,
Prof. Stevelly, Prof. G. G. Stokes.
Prof. Dixon, W. J. Blacquorn Ran
kine, Prof. Stevelly, J. Tyndall.
B. Blaydes Haworth, J. D. Sollitt,
Prof. Stevelly, J. Welsh.
J. Hartnup, H. G. Puckle, Prof.
Stevelly, J. Tyndall, J. Welsh.
Rev. Dr. Forbes, Prof. D.Gray, Prof.
Tyndall.
C. Brooke, Rev. T. A. Southwood,
Prof. Stevelly, Rev. J. C. Turnbull.
Prof. Curtis, Prof. Hennessy, P. A.
Ninnis, W. J. Macquorn Rankine,
Prof. Stevelly.
Rev. S. Earnshaw, J. P. Hennessy,
Prof. Stevelly, H.J. S.Smith, Prof.
Tyndall.
xliv
REPORT — 1885.
Date and Place
1859. Aberdeen...
1860. Oxford
1861. Manchester
1862. Cambridge
1863. Newcastle
1864. Bath
1865. Birmingham
1866. Nottingham
1867. Dundee ...
1868. Norwich ...
1869. Exeter
1870. Liverpool...
1871. Edinburgh
1872. Brighton...
1873. Bradford...
1874. Belfast
1875. Bristol
1876. Glasgow ...
1877. Plymouth...
1878. Dublin
1879. Sheffield ...
1880. Swansea ...
1881. York
1882. Southamp
ton.
1883. Southport
1884. Montreal ...
1885. Aberdeen...
Presidents
The Earl of Kosse, M.A., K.P.,
Rev. B. Price, M.A., F.E.S....
G. B. Airy, M.A., D.C.L.,
F.R.S.
Prof. G. G. Stokes, M.A.,
F.R.S.
Prof . W. J. Macquorn Rankine,
C.E., F.R.S.
Prof. Cayley, M.A., F.R.S.,
F.B.A.S.
W. Spottiswoode,M.A.,F.R.S.,
F.R.A.S.
Prof. Wheatstone, D.C.L.,
F.R.S.
Prof. Sir W. Thomson, D.C.L.,
F.R.S.
Prof. J. Tyndall, LL.D.,
F.R.S.
Prof. J. J. Sylvester, LL.D.,
F.R.S.
.J. Clerk Maxwell, M.A.,
LL.D., F.R.S.
Prof. P. G. Tait, F.R.S.E. ...
VV. De La Rue, D.C.L., F.R.S.
Prof. H. J. S. Smith, F.R.S.
Rev. Prof. J. H. Jellett, M.A..
M.R.I.A.
Prof. Balfour Stewart, M.A.,
LL.D., F.R.S.
Prof. Sir W. Thomson, M.A.,
D.C.L., F.R.S.
Prof. G. C. Foster, B.A., F.R.S.,
Pres. Physical Soc.
Rev. Prof. Salmon, D.D.,
D.C.L., F.R.S.
Geortce Johnstone Stoney,
M.A., F.R.S.
Prof. W. Grylls Adams, M.A.,
F.R.S.
Prof. Sir W. Thomson, M.A.,
LL.D., D.C.L., F.R.S.
Rt. Hon. Prof. Lord Rayleigh,
M.A., F.R.S.
L'rof . 0. Heurici, Ph.D.,F.R.S.,
Prof. Sir W. Thomson, M.A.,
LL.D., D.C.L., F.R.S
Prof. G. Chrystal, M.A.,
F.R.S.E.
Secretaries
J. P. Hennessy, Prof. Maxwell, H.
J. S. Smith, Prof. Stevelly.
Rev. G. C. Bell, Rev. T. Rennison,
Prof. Stevelly.
Prof. R. B. Clifton, Prof. H. J. S.
Smith, Prof. Stevelly.
Prof. R. B. Clifton, Prof. H. J. S.
Smith, Prof. Stevelly.
Rev.N.Ferrers,Prof.Fuller,F.Jenkin,
Prof. Stevellv, Rev. C. T. Wiitley.
Prof. Fuller, F. Jenkin, Rev. G.
Buckle, Prof. Stevelly.
Rev. T. N. Hutchinson, V. Jenkin, G.
S. Mathews, Prof. H. J. S. Smith,
J. M. Wilson.
Fleeming Jenkin, Prof. H. J.S.Smith,
Rev. S. N. Swann.
Rev. G. Buckle, Prof. G. C. Foster,
Prof. Fuller, Prof. Swan.
Prof. G. C. Foster, Rev. R. Harley,
R. B. Havward.
Prof. G. C. Foster, R. B. Hay ward,
W. K. Clifford.
Prof. W. G. Adams, W. K. Clifford,
Prof. G. C. Foster, Rev. W. Allen
Whit worth.
Prof. W. G. Adams, J. T. Bottomlev,
Prof. W. K. Clifford, Prof. J. I).
Everett, Rev. R. Harle)'.
Prof. W.K. Clifford, .LW.L.Glaisher,
Prof . A. S. Herschel, G. F. Rodwell.
Prof. W. K. Clifford, Prof. Forbes, J.
W.L. Glaisher, Prof. A. S. Herschel.
J. W. L. Glai.sher, Prof. Herschel,
Randal Nixon, J. Perry, G. F.
Rodwell.
Prof. W. F. Barrett, J. W.L. Glaisher,
C. T. Hudson, G. F. Rodwell.
Prof. W. F. liarrett, J. T. Bottomley,
Prof. G. Forbes, J. W. L. Glaisher,
T. Muir.
Prof. W. F. Barrett, J. T. Bottomley,
J. W. L. Glaisher, F. G. Landon.
Prof. J. Casey, G. F. Fitzgerald, J.
W. L. Glaisher, Dr. O. J. Lodge.
A. H. Allen, J. W. L. Glaisher,''Dr.
O. J. Lodge, D. MacAlister.
W. E. Ayrtion, J. W. L. Glaisher,
Dr. O. J. Lodge, D. MacAlister.
Prof. W. E. Ayrton, Prof. O. J. Lodge,
D. IMacAlister, Rev. W. Routh.
W. M. Hicks, Prof. O. J. Lodge,
D. MacAlister, Rev. G. Richardson.
W. M. Hicks, Prof. O. J. Lodge,
D. ilacAlister, Prof. R. C. Rowe.
C. Carpmael, W. M. Hicks, Prof. A.
Johnson, Prof. O. J. Lodge, Dr. D.
MncAlister.
R. E. Baynes, R. T. Glazebroob, Prof.
W. M. Hicks, Prof. W. Ingram.
TBESIDENTS AND SECRETAEIES OF THE SECTIONS.
xlv
CHEMICAL SCIENCE.
COMMITTEE OF SCIENCES, II. — CHEMTSTRT, MINERALOGY.
Date and Place
Presidents
1832.
18.33.
1834.
183.5.
1836.
1837.
1838.
1839.
1840.
Oxford
Cambridge
Edinburuh
■John Dalton, D.C.L., F.R.S.
; John Dalton, D.C.L., F.R.S.
Dr. Hope
Secretaries
James F. W. Johnston.
Prof. Miller.
Mr. Johnston, Dr Christison.
Dublin .
Bristol .
Liverpool...
Newcastle
Birmingham
Glasgow ...
1841. Plymouth...
1842.
1843.
1844.
1845.
1846,
1847.
1848.
1849.
1850.
1851.
1852.
Manchester
Cork
York
Cambridge
Soiithamp
ton
Oxford
SECTION B, — CHEMISTRY AND MINERALOGY.
Dr. T. Thomson, F.R.S IDr. Apjohn, Prof. Johnston.
Rev. Prof. Gumming Dr. Apjohn, Dr. C.Henry, \V. Hera
path.
Prof. Johnston, Prof. Miller, Dr.
Reynolds.
Prof. Miller, H. L. Pattinson, Thomas
Richardson.
Dr. Golding Bird, Dr. J. B. Melson.
Dr. R. D/Thomson, Dr. T. Clark,
Dr. L. Playfair.
J. Prideaux, Robert Hunt, W. M.
Tweedy.
Dr. L. Playfair, R. Hunt, J. Graham.
R. Hunt, Dr. Sweeny.
Dr. I.. Playfair, E. Solly, T. H. Barker.
R. Hunt, J. P. Joule, Prof. Miller,
E. Solly.
Dr. Miller, R. Hunt, W. Randall.
Swansea ...
Birmingham
Edinburgh
Ipswich . . .
Belfast
1853. Hull
1854.
1855.
1856.
1857.
1858.
1859.
1860.
1861,
1862.
Liverpool
Glasgow .,.
Cheltenham
Dublin
Leeds
Aberdeen...
Oxford
Manchester
Cambridge
1863. Newcastle
1864.
1865.
Bath
Birmingham
Michael Faraday, F.R.S
Rev. William Whewell,F.R.S.
Prof. T. Graham, F.R.S
Dr. Thomas Thomson, F.R.S.
Dr. Daubeny, F.R.S
John Dalton, D.C.L., F.R.S.
Prof. Apjohn, M.R.LA
Prof. T. Graham, F.R.S
Rev. Prof. Gumming
Michael Faraday, D.C.L.,
F.R.S.
Rev. W. V. Harcourt, M.A.,
F.R.S.
Richard Phillips, F.R.S
John Perc3% M.D., F.R.S
Dr. Christison, V.P.R.S.B.
Prof. Thomas Graham, F.R.S.
Thomas Andrews,M.D., F.R.S.
Prof. J. F. W. Johnston, M.A.,
F.R.S.
Prof.W. A.Miller, M.D.,F.R.S.
Dr. Lyon Playfair.C.B., F.R.S.
Prof. B. C. Brodie, F.R.S. ...
Prof. Apjohn, M.D., F.R.S.,
M.R.LA.
Sir J. F. W. Herschel, Bart.,
D.C.L.
Dr. Lyon Playfair, C.B., F.R.S.
Prof.B. C. Brodie, F.R.S
Prof. W.A.Miller, M.D.,F.R.S.
Prof. W.A.Miller, M.D.,F.R.S.
Dr. Alex. W. Williamson,
F.R.S.
W.Odling, M.B.,F.R.S.,F.C.S.
Prof. W. A. Miller, M.D.,
Y.P.R.S.
B. G. Brodie, R. Hunt, Prof. Solly.
T. H. Henry, R. Hunt, T. AVilliams.
R. Hunt, G. Shaw.
Dr. Anderson, R. Hunt, Dr. Wilson.
T. J. Pearsall, W. S. Ward.
Dr. Gladstone, Prof. Hodges, Prof.
Ronalds.
H. S. Blimdell, Prof. R. Hunt, T. J.
Pearsall.
Dr.Ed wards, Dr. Gladstone, Dr.Price.
Prof. Frankland, D). H. E. Roscoe.
J. Horsley, P. J. Worsley, Prof.
Voelcker.
Dr. Davy, Dr. Gladstone, Prof. Sul
livan.
Dr. Gladstone, W. Odling, R. Rey
nolds.
J. S. Brazier, Dr. Gladstone, G. D.
Liveing, Dr. Odling.
A. Vernon Harcourt, G. D. Liveing,
A. B. Northcote.
A. Vernon Harcourt, G. D. Liveinc.
H. W. Elphinstone, W. Odling, Prof.
Roscoe.
Prof. Liveing, H. L. Pattinson, J. C.
Stevenson.
A.V.Harcourt,Prof.Liveing,R.Biggs.
A. V. Harcourt, H. Adkiris, Prol.
Wanklyn, A. Winkler Wills.
xlvi
EEPOKT 1885.
Date and Place
1866. Nottingham
1867. Dundee ...
1868. Norwich ...
1869. Exeter
1870. Liverpool...
1871. Edinburgh
1872. Brighton..
1873. Bradford..
1874. Belfast
1875. Bristol
1876. Glasgow ..
1877. Plymouth..
1878. Dublin
1879. Sbeffield ..
1880. Swansea ..
Presidents
Secretaries
H. Bence Jones, M.D.,F.E.S.
1881. York.
1882. Southamp
ton
Prof. H. E. Roscoe, B.A.,
F.R.S., F.C.S.
Prof. T. Andrews, M.D.,F.R.S.
J. H. Atherton, Prof. Liveing, W. J.
Russell, J. White.
Prof. T. Anderson, M.D., A. Crum Brown, Prof. G. D. Liveing,
F.R.S.E. i W. J. Russell.
Prof. E. Frankland, F.R.S., Dr. A. Crum Brown, Dr. W. J. Rus
F.C.S. sell, F. Sutton.
Dr. H. Debus, F.R.S., F.C.S. Prof. A. Crum Brown, Dr. W. J.
Russell, Dr. Atkinson.
Prof. A. Crum Brown. A. E. Fletcher,
Dr. W. J. Russell.
J. T. Buchanan, W. N. Hartley, T.
E. Thorpe.
Dr. J. H. Gladstone, F.R.S.... Dr. Mills, W. Chandler Roberts, Dr.
! W. J. Russell, Dr. T. Wood.
Prof. W. J. Russell, F.R.S.... , Dr. Armstrong, Dr. Mills, W. Chand
J ler Roberts, Dr. Thorpe.
Prof. A. Crum Brown, M.D., Dr. T. Cranstoun Charles, W. Chand
F.R.S.E., F.C.S. I ler Roberts, Prof. Thorpe.
A. G. Vernon Harcourt, M.A., Dr. H. E. Armstrong, W. Chandler
F.R.S., F.C.S. 1 Roberts, W. A. Tilden.
W. H. Perkin, F.R.S W. Dittmar, W. Chandler Roberts,
J. M. Thomson, W. A. Tilden.
F. A. Abel, F.R.S., F.C.S. ... Dr. Oxland. W. Cliandler Roberts,
I J. M. Thomson.
Prof. Maxwell Simpson, M.D.,'W. Chandler Roberts, J. M. Thom
F.R.S., F.C.S. I son. Dr. C. R. Tichborne, T. Wills.
Prof. Dewar, M.A., F.R.S. IH. S. Bell, W. Chandler Roberts, J.
M. Thomson.
Joseph Henry Gilbert, Ph.D.,' H. B. Dixon, Dr. W. R. Eaton Hodg
F.R.S. kinson, P. Phillips Bedson, J. M.
Thomson.
Prof. A. W.Williamson, Ph.D., P. Phillips Bedson, H. B. Dixon,
F.R.S. 1 T. Gough.
Prof. G. D. Liveing, M.A., P. Phillips Bedson, H. B. Dixon,
F.R.S. I J. L. Notter.
1883. Southport Dr. J. H. Gladstone, F.R.S... I Prof. P. Phillips Bedson, H. B.
' ! Dixon, H. Forster Morley.
1884. Montreal ... Prof. Sir H. E. Roscoe, Ph.D., Prof. P. Phillips Bedson, H.B. Dixon,
LL.D., F.R.S. T. McFarlane, Prof. W. H. I'ikc.
188.'5. Aberdeen... Prof. H. E. Armstrong, Ph.D., Prof. P.Phillips Bedson, H. B. Dixon,
I F.R.S., Sec. C.S. : H. Forster Morley, Dr. W. J.
I I Simpson.
GEOLOGICAL (and, until 1851, GEOGRAPHICAL) SCIENCE.
COMMITTEE OF SCIENCES, III. — GEOLOGY AND GEOGKAPHY.
1832. Oxford IR. L Murchi.sou, F.R.S ^ John Taylor.
1833. Cambridge. !g. B. Greenough, F.R.S W. Lonsdale, John Phillips.
1834. Edinburgh .[Prof. Jameson ! Prof . Phillips, T. Jameson Torrie,
i Rev. J. Yates.
1835. Dublin.
1836. Bristol .
1837. Liverpool...
SECTION C. — GEOLOGY AND GEOGKAPHY.
R. J. Griffith ; Captain Portlock, T. J. Torrie.
Rev. Dr. Buckland, F.R.S. — William Sanders, S. Stutchbury,
6^e(>(/>'ff/^7i!y, R. L Murchison, ! T.J. Torrie.
F.R.S. j
Rev. Prof. Sedgwick, F.R.S.— ; Captain Portlock, R. Hunter. — Geo
Geoffrap7iy,G.'B.GYeenough, fjraphy, Captain H. M. Denham,
F.R.S. R.N.
PRESIDENTS AND SECRETARIES OF THE SECTIONS.
xlvii
Date and Place
1838. Newcastle. .
1839. Birmingham
1S40. Glasgow ...
1811. Plymouth...
1842. Manchester
1843. Cork
1844. York
1845. Cambridge.
1846. Southamp
ton.
1847. Oxford
1848. Swansea ...
1 849.Birmingham
1850. Edinburgh'
Presidents
C. Lyell, F.K.S., V.P.G.S.—
Geoqraphy, Lord Prudhope.
Kev. i)r. Buckland, F.R.S.—
Gcoqraphy, G.B.Greenough,
F.R.S.
Charles Lyell, F.R.S.— C'ert
graj>hy, G. B. Greenough,
F.R.S.
H. T. Dela Beche, F.R.S. ...
R. I. Mmchison, F.R.S
Richard E. Griffith, F.R.S.,
M.R.LA.
Henry Warbuiton, M.P.,Pres.
Geol. Soc.
Rev. Prof. Sedgwick, M.A.,
F.R.S.
Leonard Horner,F.R.S. — Geo
graphy, G. B. Greenough,
F.R.S.
Very Rev.Dr.Buckland,F.R.S.
Sir H. T. De la Beche, C.B.,
F.R.S.
Sir Charles Lyell, F.R.S.,
F.G.S.
Sir Roderick I. Murchison,
F.R.S.
Secretaries
W. C. Trevelyan, Capt. Portlock. —
Geoqraphy, Capt. Washington.
George Lloyd, M.D., H. E. Strick
land, Charles Darwin.
W. J. Hamilton, D. Milne, Hugh
Murray, H. E. Strickland, John
Scoular, M.D.
W. J. Hamilton, Edward Moore, M.D.,
R. Hutton.
E. W. Binney, R. Hutton, Dr. R.
Lloyd, H. E. Strickland.
Francis M. Jennings, H. E. Strick
land.
Prof. Ansted, E. H. Bunbury.
Rev. J. C. Gumming, A. C. Ramsay,
Rev. W. Thorp.
Robert A. Austen, Dr. J. H. Norton,
Prof. Oldham. — Geoyrajjhy, Dr. C.
T. Beke.
Prof. Ansted, Prof. Oldham, A. C.
Ramsay, J. Ruskin.
Starling Benson, Prof. Oldham,
Prof. Ramsay.
J. Beete Jukes, Prof. Oldham, Prof.
A. C. Ramsay.
A. Keith Johnston, Hugh Miller,
Prof. Nicol.
1851. Ipswich
1852. Belfast.
1853. Hull
1854. Liverpool . .
1855. Glasgow ...
1856. Cheltenham
1857. Dublin
1858. Leeds
1859. Aberdeen...
1860. Oxford
1861. Manchester
1862. Cambridge
SECTION c (^continued'). — geology.
WilliamHopkins, M. A.,F.R.S.
LieutCol. Portlock, R.E.,
F.R.S.
Prof. Sedgwick, F.R.S
Prof. Edward Forbes, F.R.S.
Prof. A. C. Ramsay, F.R.S....
The Lord Talbot de Malahide
C. J. F. Bunbuiy, G. W. Ormerod,
Searles Wood.
James Bryce, James MacAdam,
Prof. M'Coy, Prof. Nicol.
Prof. Harkness, William Lawton.
John Cunningham, Prof. Harkness,
G. W. Ormerod, J. W. Woodall.
Sir R. I. Murchison, F.R.S.... James Bryce, Prof. Harkness, Prof.
Nicol.
Rev. P. B. Brodie, Rev. R. Hep
worth, Edward Hull, J. Scougall,
T. Wright.
Prof. Harkness, Gilbert Sanders,
Robert H. Scott.
William Hopkins,M.A.,LL.D., Prof. Nicol, H. C. Sorby, E. W.
F.R.S. Shaw.
Sir Charles Lyell, LL.D., Prof. Harkness, Rev. J. Longmuir,
D.C.L., F.R.S. j H. C. Sorby.
Rev. Prof. Sedgwick, LL.D.,! Prof. Harkness, Edward Hull, Capt.
F.R.S., F.G.S. D. C. L. Woodall.
Sir R. I. Murchison, D.C.L., Prof. Harkness, Edward Hull, T.
LL.D., F.R.S. Rupert Jones, G. W. Ormerod.
J. Beete Jukes, M.A., F.R.S. Lucas Barrett, Prof. T. Rupert
Jones, H. C. Sorby.
' At a meeting of the General Committee held in 1850, it was resolved ' That
the subject of Geography be separated from Geology and combined with Ethnology,
to constitute a separate Section, under the title of the " Geographical and Ethno
logical Section," ' for Presidents and Secretaries of which see page lii.
xlviii
EEPORT — 1885.
Date and Place
1863. Newcastle
1864. Bath
1865. Birminghani
1866. Nottingham
1867. Dundee ...
1868. Norwich ...
1869. Exeter
1870. Liverpool...
1871. Edinburgh
1872. Brighton...
187.3. Bradford...
1874. Belfast
1875. Bristol
1876. Glasgow ..
1877. Plymouth...
1878. Dublin
1879. Sheffield ...
1880. Swansea ...
1881. York
1882. Southamp
ton.
1883. Southport
1884. Montreal ...
1885. Aberdeen...
Presidents
Secretaries
Prof. Warington W. Smyth,
F.R.S., F.G.S,
Prof. J. Phillips, LL.D.,
F.E.S., F.G.S.
Sir R. I. MurchisoD, Bart.,
K.C.B.
Prof. A. C. Ramsay. LL.D.,
F.R.S.
Archibald Geikie, F.R.S.,
F.G.S.
R. A. C. GodwinAusten,
F.R.S., F.G.S.
Prof. R. Harkness, F.R.S.,
F.G.S.
SirPhilipde M.Grey Es^erton,
Bart., M.P., F.R.S.
Prof. A. Geikie, F.R.S., F.G.S.
R. A. C. GodwinAusten,]
F.R.S., F.G.S.
Prof. J. Phillips, D.C.L.,
F.R.S., F.G.S.
Prof. Hull, M.A., F.R.S.,
F.G.S.
Dr. Thomas Wright, F.R.S.E.,
F.G.S.
Prof. John Yoiing, M.D
W. Pengelly, F.R.S
.John Evans, D.C.L., F.R.S.,
F.S.A., F.G.S.
Prof. P. Martin Duncan, M.B.,
F.R.S., F.G.S.
H. C. Sorby, LL.D., F.R.S.,
F.G.S.
A. C. Ramsay, LL.D., F.R.S.,
V c ^
R. Etheridge, F.R.S., F.G.S.
Prof. W. C. Williamson,
LL.D., F.R.S.
W. T. Blanford, F.R S., Sec.
G.S.
Prof. .7. W. Judd, F.R.S., Sec.
G.S.
E. F. Boyd, John Daglish, H. C.
Sorbv, Thomas Sopwith.
W. B. Dawkins, J. Johnston, H. C.
Sorbj', W. Pengelly.
Rev. P. B. Brodie, J. Jones, Rev. E.
Myers, H. C. Sorby, W. Pengelly.
R. Etheridge, W. Pengelly, T. Wil
son, G. H. Wright.
Edward Hull, W. Pengelly, Henry
Woodward.
Rev. 0. Fisher, Rev. J, Gunn, W.
Pengelly, Eov. H. H. Wiuwood.
W. Pengelly, W. Boyd Dawkins.
Rev. n. H. Winwood.
W. Pengelly, Rev. H. H. Winwood,
W. Boyd Dawkins, G. H. Morton.
R. Etheridge, J. Geikie, T. McKennv
Hughes, L. C. Miall.
L. C. Miall, George Scott, William
Topley, Henry Woodward.
L. C. Miall, R. H. Tiddeman, W.
Topley.
F. Drew, L. C. Jliall, R. G. Symes,
R. H. Tiddeman.
L. C. Miall, E. B. Tawney, W. Top
ley.
J. Armstrong, F. W. Rudler, W.
Topley.
Dr. Le Neve Foster, R. H. Tidde
man, W. Topic)'.
E. T. Hardman, Prof. J. O'Reill},
R. H. Tiddeman.
W. Topley, G. Blake Walker.
W. Topley, W. Whitaker.
J. E. Clark, W. Keeping, W. Topley,
W. Whitaker.
T. AV. Shore, W. Topley, E. West
lake, W. Whitaker.
R. Betley, C. E. De Ranee, W. Top
ley, W. Whitaker.
F. Adams, Prof. E. W. Claypole, W.
Topley, W. Whitaker.
C. E. De Ranee. J. Horne, J. J. H.
1 Teall, W. Topley.
BIOLOGICAL SCIENCES.
COMMITTEE Of SCIENCES, IV. — ZOOLOGY, BOTANY, PHYSIOLOGY, ANATOMY.
1832. Oxford lEev. P. B. Duncan, F.G.S. ...IRev. Prof. J. S. Henslow.
1833. Cambridge' Rev. W. L. P. Garnons, F.L.S. ' C. C. Babinglon, D. Don.
1834. Edinburgh. Prof. Graham W. Yarrell, Prof. Burnett.
' At this Meeting Physiology and Anatomy were made a separate Committee,
for Presidents and Secretaries of which see p. li.
PRESIDENTS AND SECBETAEIES OF THE SECTIONS.
SECTION D. — ZOOLOGT AND BOTANY.
xlix
Date and Place
Presidents
1835. Dublin.
1836. Bristol.
Dr. Allman
Rev. Prof. Henslow
1837. Liverpool...
1838. Newcastle
1 839. Birmingham
1840. Glasgow ...
1841. Plymouth...
1842. Manchester
W. S. MacLeay
Sir W. Jardine, Bart.
Prof. Owen, F.R.S
Sir W. J. Hooker, LL.D.
1843. Cork.
1844. York.
1845. Cambridge
1846. Southamp
ton.
1847. Oxford
John Richardson, M.D., F.R.S.
Hon. and Very Rev. W. Her
bert, LL.D., F.L.S.
William Tliompson, F.L.S. ...
Very Rev. the Dean of Man
chester.
'Rev. Prof. Henslow, F.L.S....
I Sir J. Richardson, M.D.,
j T? T? S
H. E. Strickland, M.A., F.R.S.
Secretaries
J. Curtis, Dr. Litton.
J. Curtis, Prof. Don, Dr. Riley, S.
Eootsey.
C. C. Babington, Rev. L. Jenyns, W.
Swainson.
J. E. Gray, Prof. Jones, R. Owen,
Dr. Richardson.
E. Forbes, W. Ick, R. Patterson.
Prof. W. Couper, E. Forbes, R. Pat
terson.
J. Couch, Dr. Lankester, R. Patterson.
Dr. Lankester, E. Patterson, J. A.
Turner.
G. J. Allman, Dr. Lankester, R.
Patterson.
Prof. Allman, H. Goodsir, Dr. King,
Dr. Lankester.
Dr. Lankester, T. V. Wollaston,
Dr. Lankester, T. V. Wollaston, H.
Wooldridge.
Dr. Lankester, Dr. Melville, T. V.
Wollaston.
1849. Birmingham
1850. Edinburgh
1851. Ipswich ...
1852. Belfast
1853. Hull
1854. Liverpool...
1855. Glasgow ...
1856. Cheltenham
1857. Dublin
1858. Leeds
1859. Aberdeen...
1860. Oxford
1861. Manchester
1862. Cambridge
1863. Newcastle
1864. Bath
1865. Birmingham
1885.
William Spence, F.R.S
Prof. Goodsir, F.R.S. L. & E.
Rev. Prof. Henslow, M.A.,
F.R.S.
W. Ogilby
SECTION D (contimied). — zooLoor and botany, including physiology.
[For the Presidents and Secretaries of the Anatomical and Physiological Subsec
tions and the temporary Section E of Anatomy and Medicine, see p. li.]
1848. Swansea ... L. W. Dillwyn, F.R.S Dr. R. Wilbraham Falconer, A. Hen
frey. Dr. Lankester.
Dr. Lankester, Dr. Russell.
Prof. J. H. Bennett, M.D., Dr. Lan
kester, Dr. Douglas Maclagan.
Prof. Allman, F. W. Johnston, Dr. E.
Lankester.
Dr. Dickie, George C. Hyndman, Dr.
Edwin Lankester.
Robert Harrison, Dr. E. Lankester.
Isaac Byerley, Dr. E. Lankester.
William Keddie, Dr. Lankester.
Dr. J. Abercrombie, Prof. Buckman,
Dr. Lankester.
Pro^:. J. R. Kinahan, Dr. E. Lankester,
Robert Patterson, Dr. W. E. Steele.
Henry Denny, Dr. Heaton, Dr. E.
Lankester, Dr. E. Perceval Wright.
Prof. Dickie, M.D., Dr. E. Lankester,
Dr. Ogilvy.
W. S. Church, Dr. E. Lankester, P,
L. Sclater, Dr. E. Perceval Wright.
Dr. T. Alcock, Dr. E. Lankester, Dr.
P. L. Sclater, Dr. E. P. Wright.
Alfred Newton, Dr. E. P. Wright.
Dr. E. Charlton, A. Newton, Rev. H.
B. Tristram, Dr. E. P. Wright.
H. B. Brady, C. E. Broom," H. T.
Stainton, Dr. E. P. Wright.
Dr. J. Anthony, Rev. C. Clarke, Rev.
H. B. Tristram, Dr. E. P. Wright.
c
C. C. Babington, M.A., F.R.S.
Prof. Balfour, M.D., F.R.S....
Rev. Dr. Fleeming, F.R.S.E.
Thomas Bell, F.R.S., Pres.L.S.
Prof. W. H. Harvey, M.D.,
F.R.S.
C. C. Babington, M.A., F.R.S.
Sir W. Jardine, Bart., F.R.S.E.
Rev. Prof. Henslow, F.L.S....
Prof. C. C. Babington, F.R.S.
Prof . Huxley, F.R.S
Prof. Balfour, M.D., F.R.S....
Dr. John E. Gray, F.R.S. ...
T. Thomson, M.D., F.R.S. ...
REPORT — 1885.
SECTION D {continued). — biologt.'
Date and Place
1866. Nottingham
1867. Dundee
1868. Norwich
1869. Exeter.
1870. Liverpool.
1871. Edinburgh
1872. Brighton
1873. Bradford
1874, Belfast .
1875. Bristol
1876. Glasgow
1877. Plymouth..
Presidents
Prof. Hiixley, LL.D., F.R.S.
— Pliijsiulo/i'ical Dcj>., Prof.
Humphry," M.D., F.R.S.—
Aiithropohf/ieal I)vp., Alf.
K. Wallace, F.R.G.S.
Prof. Sharpey, M.D., Sec. R.S.
— Bcj). of Zool. and Bat.,
George Busk, M.D., F.K.8.
Rev. M. J. Berkeley, F.L.S.
— Dvp. of Physiohfiy, W.
H. Flower, F.R.S.
George P.usk, F.R.S., F.L.S.
— Dcp. of Hot. and Zool.,
C. Spence Bate, F.R.S. 
Dc2>. of Ethno., E. B. Tylor.
Prof.G. iRolle.ston,M.A., M.D.,
F.R.S., Y.l^.'S. — Bcj). of
Aiiat. and P/ii/mil.,FTot.M.
P'oster, M.D., F.L.S.— i>(y.
of Ethno., J. Evans, F.R.S.
Prof. Allen Thomson, M.D.,
¥.IX.^.—Dep. of Bot. and
.^w*^.,rrof.WyvilleThomson,
F.R.S.— Z'cy;. of Antfirojwl.,
Prof. W. Turner, M.D.
Sir J. Lubbock, Bart., F.R.S.—
Bej). of Anut. and Physiol.,
Dr. Burdon Sanderson,
F.R.S.— Z)<y». ofAnthrojwl,
Col. A. Lane Fox, F.G.S.
Prof. Allman, F.R.S.— Brj>. of
A nat.and Physiol. ,Vr:oi. Ru
therford, M.D. — BvpofAn
thropol.. Dr. Beddoe, F.R.S.
Prof. Redfern, M..V).—B(p. of
Zool. and Bot., Dr. Hooker,
C.B.,Pres.R.S.— i>(7Ao/^«
throp., Sir W.R.Wilde, M.D.
P. L. Sclater, F.R.S.— Z**^. o/
.1 nat.and Ph ifsiol.,Vr:oi.C\Q
land, M.D., V.H.'&.—Bep.of
Anthropol., Prof. Rolleston,
M.D., F.R.S.
A. Russel Wallace, F.R.G.S.,
F.L.S.— i?(y. of Zool. and
Bot., Prof. A. Newton, M.A.,
¥.B,.S.—Bep. of Anat. and
Phi/siol, Dr. J. G. McKen
drick, P.R.S.E.
.J.awynJeffreys,LL.D.,F.R.S.,
F.L.S. — Bep. of Anat. and
Phy.noL, Prof. Macalister,
Secretaries
Dr. J. Beddard, W. Felkin, Rev. H.
B. Tristram, W. Turner, E. B.
Tylor, Dr. E. P. Wright.
C. Spence Bate, Dr. S. Cobbold, Dr.
U. Foster, H. T. Stainton, Rev. H.
B. Tristram, Prof. W. Turner.
Dr. T. S. Cobbold, G. W. Firth, Dr.
M. Foster, Prof. Lawson, H. T.
Stainton, Rev. Dr. H. B. Tristram,
Dr. E. P. Wrisrht.
Dr. T. S. Cobbold, Prof. M. Foster,
E. Ray Lankester, Prof. Lawson,
H. T Stainton, Rev. H. B. Tris
tram.
Dr. T. S. Cobbold, Sebastian Evans,
Prof. Lawson, Thos. J. Moore, H.
T. Stainton, Rev. H. B. Tri.stram,
C. Staniland Wake, E. Ray Lan
kester.
Dr. T. R. Eraser, Dr. Arthur Gamgee,
E. Ray Lankester, Prof. Lawson,
H. T. Stainton, C. Staniland Wake,
Dr. W. Rutherford, Dr. Kelburne
King.
Prof. ThiseltonDyer, H. T. Stainton,
Prof. Lawson, F. W. Rudler, J. H.
Lamprey, Dr. Gamgee, E. Ray
Lankester, Dr. PyeSmith.
Prof. ThiseltonDyer, Prof. Lawson,
R. JI'Lachlan, Dr. PyeSmith, E.
Ray Lankester, F. W. Rudler, J.
H. Lamprey.
W.T. Thiselton Dyer, R. O. Cunning
ham, Dr. J. J. Charles, Dr. P. H.
PyeSmith, J. J. Murphy, F. W.
Rudler.
E. R. Alston, Dr. McKendrick, Prof.
W. R. M'Nab, Dr. Martyn, F. W.
Rudler, Dr. P. H. PyeSmith, Dr.
W. Spencer.
E. R. Alston, Hvde Clarke, Dr
Knox, Prof. W." R. M'Nab, Dr.
Muirhead, Prof. Morrison Wat
son.
E. R. Alston, F. Brent, Dr. D. J
Cunningham, Dr. C. A. Hingston,
Prof. W. R. M'Nab, J. B. Rowe,
F. W. Rudler.
M.D.~Bep. of Anthropol.,
Francis Galton, M.A.,F.R.S.
' At a meeting of the General Committee in 1865, it was resolved : — ' That the title
of Section D be changed to Biology ; ' and ' That for the word " Subsection," in the
rules for conducting thebusiness of the Sections, the word "Department" be substituted.'
PRESIDENTS AND SECRETARIES OF THE SECTIONS.
li
Date and Place
1878. Dublin ,
1879. Sheffield ...
1880. Swansea
1881. York.
1882. Southamp
ton.
1883. Southport'
1884. Montreal...
1885. Aberdeen...
'Presidents
Prof. W. H. Flower, F.R.S.—
Bcp. of AnthrojMl., Prof.
Huxley, Sec. R.S. — Bip.
of A/iat. and Physiol., R.
McDonnell, M.D., F.R.S.
Prof. St. George Mivart,
F.R.S.— Z)e/A 4 Anthropol.,
E. B. Tylor, D.C.L., F.R.S.
— Bep. of Anat. and Phi/
mil.. Dr. PyeSmith.
A. C. L. Giinther, M.D., F.R.S.
— Dcp. of Anat. and Phy
siol, F. M. Balfour, M.A.,
F.'R.S.—Bep. of Antkropol.,
F. W. Rudler, F.G.S.
Richard Owen, C.B., M.D.,
F.R.S.^Bep.of AnthropoL,
Prof. W. H. Flower, LL.D.,
F.R.S.— 2)<7A of Anat. and
Phymol.,YToi.J. S. Burden
Sanderson, M.D., F.R.S.
Prof. A. Gamgee, M.D., F.R.S.
 Bep. of Zool. and Bot.,
Prof. M. A. Lawson, M.A.,
F.Jj.S.— Bep. of Anthropol.,
Prof. W. Boyd Dawkins,
M.A., F.R.S.
Prof. E. Ray Lankester, M.A.,
F.R.S.— D^jy;. of Anthropol.,
W. Pengelly, F.R.S.
Prof. H. N. Moseley, M.A.,
F.R.S.
Prof. W. C. Mcintosh, M.D.,
LL.D., F.R.S. L. & E.
Secretaries
Dr. R. J. Harvey, Dr. T. Hayden,
Prof. W. R. M'Nab, Prof. J. M.
Purser, J. B . Rowe, F. W. Rudler.
Arthur Jackson, Prof. W. R. M'Nab,
J. B. Rowe, F. W. Rudler, Prof.
Schiifer.
G. W. Bloxam, John Priestley,
Howard Saunders, Adam Sedg
wick.
G. W. Bloxam, W. A. Forbes, Rev.
W. C. Hey, Prof. W. R. M'Nab,
W. North, John Priestley, Howard
Saunders, H. E. Spencer.
G. W. Bloxam, W. Heape, J. B.
Nias, Howard Saunders, A. Sedg
wick, T. W. Shore, jun.
G. W. Bloxam, Dr. G. J. Haslam,
W. Heape, W. Hurst, Prof. A. M.
Marshall, Howard Saunders, Dr.
G. A. Woods.
Prof. W. Osier, Howard Saunders, A.
Sedgwick, Prof. R. R. Wright.
W. Heape, J. McGregor Robertson,
J. Duncan Matthews, Howard
Saunders, H. Marshall Ward.
ANATOMICAL AND PHYSIOLOGICAL SCIENCES.
COMMITTEE OF SCIENCES, V. — ANATOMY AND PHYSIOLOGY.
1833. Cambridge Dr. Haviland iDr. Bond, Mr. Paget.
1834. Edinburgh Dr. Abercrombie iDr. Roget, Dr. William Thomson.
SECTION E (until 1847). — ANATOMY AND MEDICINE.
183.5. Dublin
1836. Bristol
1887. Liverpool...
1838. Newcastle
1839. Birmingham
1840. Glasgow ...
1841. Plymouth...
Dr. Pritchard
Dr. Roget, F.R.S
Prof. W. Clark, M.D.
T. E. Headlam, M.D
John Yelloly, M.D., F.R.S...
James Watson, M.D
P. M. Roget, M.D., Sec. R.S.
Dr. Harrison, Dr. Hart.
Dr. Symonds.
Dr. J. Carson, jun., James Long,
Dr. J. R. W. Vose.
T. M. Greenhow, Dr. J. R. W. Vose.
Dr. G. O. Rees, F. Ryland.
Dr. J. Brown, Prof. Couper, Prof
Reid.
Dr. J. Butter, J. Fuge, Dr. R. R
Sargent.
' By direction of the General Committee at Southampton (1882) the Departments
■of Zoology and Botany and of Anatomy and Physiology were amalgamated.
By authority of the General Committee, Anthropology was made a separate
Section, for Presidents and Secretaries of which see p. Ivii.
c2
lii
REPORT 1885.
SECTION E. PHYSIOLOGY.
Date and Place
1842. Manchester
1843. Cork
1844 York
1845. Cambridge
1846. Southamp
ton.
1847. Oxford' ...
Presidents
Secretaries
Edward Holme, M.D., F.L.S.'Dr. Cliaytor, Dr. R. S. Sargent.
Sir James Pitcairn, M.D.
J. C. Pritchard, M.D
Prof. J. Haviland, M.D. .
Prof. Owen, M.D., F.R.S.
Prof. Ogle, M.D., F.R.S. .
Dr. John Popham, Dr. R. S. Sargent.
I. Erichsen, Dr. R. S. Sargent.
Dr. R. S. Sargent, Dr. Webster.
C. P. Keele, Dr. Laycock, Dr. Sar
gent.
Dr. Thomas K. Chambers, W. P.
Ormerod.
1850.
1855.
1857.
1858,
1859.
1860.
1861.
1862.
1863.
1864.
1865.
Edinburgh
Glasgow ...
Dublin
Leeds
Aberdeen...
Oxford
Manchester
Cambridge
Newcastle
Bath
Birming
ham.^
PHYSIOLOGICAL SUBSECTIONS OF SECTION D.
Prof. Bennett, M.D., F.R.S.E.
Prof. Allen Tliomson, F.R.S.
Prof. R. Harrison, M.D
Sir Benjamin Brodie, Bart.,
F.R.S.
Prof. Sliarpev, M.D., Sec.R.S.
Prof. G. RoUeston, M.D.,
F.L.S.
Dr. John Davy, F.R.S.L.& E.
G. E. Paget, M.D
Prof. Rolleston, M.D., F.R.S.
Dr. Edward Smith, LL.D.,
F.R.S.
Prof. Acland, M.D., LL.D.,
F.R.S.
Prof. J. H. Corbett, Dr. J. Struthers.
Dr. R. D. Lyons, Prof. Redfern.
C. G. Wheelhouse.
Prof. Bennett, Prof. Redfern.
Dr. R. M'Donnell, Dr. Edward
Smith.
Dr. W. Roberts, Dr. Edward Smith.
G. F. Helm, Dr. Edward Smith.
Dr. D. Embleton, Dr. W. Turner.
J. S. Bartrum, Dr. W. Turner.
Dr. A. Fleming, Dr. P. Hesiop,
Oliver Pembleton, Dr. W. Turner.
GEOGRAPHICAL AND ETHNOLOGICAL SCIENCES.
[For Presidents and Secretaries for Geography previous to 1851, see Section C, ,
p. xlvi.]
ETHNOLOGICAL SUBSECTIONS OF SECTION D.
1846. Southampton
1847. Oxford
1848. Swansea ...
1849. Birmingham
1850. Edinburgh
Dr. Pritcliard Dr. King.
Prof. H. H. Wilson, M.A.
Prof. Buckley.
G. Grant Francis.
Dr. R. G. Latham.
Daniel Wilson.
ViceAdmiral Sir A. Malcolm
SECTION E. — GEOGRAPHY AND ETHNOLOGY.
R. Cull, Rev. J. W. Donaldson, Dr.
Norton Shaw.
R. Cull, R. MacAdam, Dr. Norton
Shaw.
R. Cull, Rev. H. W. Kemp, Dr.
Norton Shaw.
Richard Cull, Rev. H. Higgins, Dr.
Hine, Dr. Norton Shaw.
Dr. W. G. Blackie, R. Cull, Dr.
Norton Shaw.
R. Cull, F. D. Hartland, W. H.
Rumsey, Dr. Norton Shaw.
R. Cull, S. Ferguson, Dr. R. R.
Madden, Dr. Norton Shaw.
' By direction of the General Committee at Oxford, Sections D and E were
incorporated under tlic name of ' Section D — Zoology and Botany, including Phy
siology ' (see p. xlix). The Section lieing then vacant was assigned in 1851 to
Geography. * Vide note on page 1.
1851.
Ipswich ...
1852.
Belfast
1853.
Hull
1854.
Liveipool...
18.55.
Glasgow ...
1856.
Cheltenham
1857.
Dublin
Sir R. I. Murchison, F.R.S.,
Pres. R.G.S.
Col. Chesney, R.A., D.C.L.,
F.R.S.
R. G. Latham, M.D., F.R.S.
Sir R. I. Murchison, D.C.L.,
F.R.S.
Sir J. Richardson, M.D.,
F.R.S.
Col. Sir H. C. Rawlinson,
K.C.B.
Rev. Dr. J. Henthorn Todd,
Pres. R.I.A.
PRESIDENTS AND SECRETARIES OF THE SECTIONS.
liii
Date and Place
1858. Leeds
1859. Aberdeen...
1860. Oxford
1861. Manchester
1862. Cambridge
1863. Newcastle
1864. Bath
1865. Birmingham
1866. Nottingham
1867. Dundee ...
1868. Norwich ...
Presidents
Sir R.I. Mmchison,G.C.St.S.,
F.R.S.
Rear  Admiral Sir James
Clerk Ross, D.C.L., F.R.S.
Sir R. I. Murchison, D.C.L..
F.R.S.
John Crawfvird, F.R.S
Francis Galton, F.R.S
Sir R. I. Murchison, K.C.B.,
F.R.S.
Sir R. I. Murchison, K.C.B.,
F.R.S.
MajorGeneral Sir H. Raw
linson, M.P., K.C.B., F.R.S.
Sir Charles Nicholson, Bart..
LL.D.
Sir Samuel Baker, F.R.G.S.
Capt. G. H. Richards, R.X.
F.R.S.
Secretaries
R. Cull, Francis Galton, P. O'Cal
laghan. Dr. Norton Shaw, Thomas
Wright.
Richard Cull, Prof.Geddes, Dr. Nor
ton Shaw.
Capt. Burrows, Dr. J. Himt, Dr. C.
Lempri^re, Dr. Norton Shaw.
Dr. J. Hunt, J. Kingsley, Dr. Nor
ton Shaw, W. Spottiswoode.
J. W. Clarke, Rev. J. Glover, Dr.
Hunt, Dr. Norton Shaw, T.
Wright.
C. Carter Blake, Hume Greenfield,
C. R. Markham, R. S. Watson.
H. W. Bates, C. R. Markham, Capt,
R. M. Murchison, T. Wright.
H. W. Bates, S. Evans, G. Jabet, C.
R. Markham, Thomas Wright.
H. W. Bates, Rev. E. T. Cusins, R.
H. Major, Clements R. JIarkham,
D. W. Nash, T. Wright.
H. W. Bates, Cyril Graham, Clements
R. Markham, S. J. Mackie, R.
Sturrock.
T. Baines, H. W. Bates, Clements R.
Markham, T. Wright.
1869. Exeter
1870. Liverpool..
1871. Edinburgh
1872. Brighton..
1873. Bradford..
1874. Belfast
1875. Bristol
1876. Glasgow ..
1877. Plymouth..
1878. Dublin
1879. Sheffield ..
1880. Swansea ..
1881. York
1882. Southamp
ton.
SECTION E {continued). 
Sir Bartle Frere, K.C.B.,
LL.D., F.R.G.S.
Sir R. I.Murcbison,Bt.,K.C.B.,
LL.D., D.C.L., F.R.S., F.G.S.
Colonel Yule, C.B., F.R.G.S.
Francis Galton, F.R.S
Sir Rutherford Alcock, K. C.B.
Major Wilson, R.E., F.R.S.,
F.R.G.S.
Lieut.  General Strachey,
R.E.,C.S.I.,F.R.S.,F.R.G.S.,
F.L.S., F.G.S.
Capt. Evans, C.B., F.R.S
Adm.SirE. Ommanney, C.B.,
F.R.S., F.R.G.S., F.R.A.S.
Prof. Sir C. Wyville Thom
son, LL.D., F.R.S.L.&E.
Clements R. Markham, C.B.,
F.R.S., Sec. R.G.S.
Lieut.Gen. Sir J. H. Lefroy,
C.B., K.C.M.G., R.A., F.R.S.,
Th' T? P S
Sir J. b.' Hooker, K.C.S.L,
C.B., F.R.S.
Sir R. Temple, Bart., G.C.S.I.,
F.R.G.S.
GEOGRAPHY.
H. W. Bates, Clements R. Markham,
J. H. Thomas.
H.W.Bates, David Buxton, Albert J.
Mott, Clements R. Markham.
Clements R. Markham, A. Buchan,
J. H. Thomas, A. Keith Johnston.
H. W. Bates, A. Keith Johnston,
Rev. J. Newton, J. H. Thomas.
H. W. Bates, A. Keith Johnston,
Clements R. Markham.
E. G. Ravenstein, E. C. Rye, J. H.
Thomas.
H. W. Bates, E. C. Rye, F. F.
Tuckett.
H. W. Bates, E. C. Rye, R. Oliphant
Wood.
H. W. Bates, F. E. Fox, E. C. Rye.
John Coles, E. C. Rye.
H. W. Bates, C. B. D. Black, E. C.
Rye.
H. W. Bates, E. C. Rye.
J. W. Barry, H. W. Bates.
E. G. Ravenstein, E. C. Eye.
liv
EEPORT — 1885.
Date and Place
Presidents
Secretaries
1883. Southport
1884. Montreal ..
1885. Aberdeen.,
Lieut.Col. H. H. Godwin
I Austen, F.R.S.
Gen. Sir J. H. Lefroy, C'.B.,
K.C.M.G., F.R.S.,Y.P.R.G.S.
Gen. J. T. Walker, C.B., R.E.,
LL.D., F.E.S.
John Coles, E. G. Eavenstein, E. C.
Rye.
Rev. Abbe Laflamme, J. S. O'Halloran,
E. G. Ravenstein, J. F. Torrance
J. S. Keltie, J. S. O'Halloran, E. G.
Ravenstein, Rev. G. A. Smith.
1833.
1834,
STATISTICAL SCIENCE.
COMMITTEE OF SCIENCES, VI. — STATISTICS.
Cambridge! Prof. Babbage, F.R.S i J. E. Drinkwater.
Edinburgh I Sir Charles Lemon, Bart  Dr. Cleland, C. Hope Maclean.
SECTION F.— STATISTICS.
1835.
1836.
1837.
1838.
1839.
1840.
1841
1842.
1843.
1844.
1845.
1846.
1847.
1848.
1849.
1850.
1851.
1852.
1853.
1854.
1855.
Dublin
Bristol
Liverpool...
Newcastle
Birmingham
Glasgow ...
Pljinouth...
Manchester
Cork
York
Cambridge
Southamp
ton.
Oxford
Swansea ...
Birmingham
Edinburgh
Ipswich ...
Belfast
Hull
Liverpool...
Glasgow ...
Charles Babbage, F.R.S
Sir Chas. Lemon, Bart., F.R.S.
Rt. Hon. Lord Sandon
Colonel Sykes, F.R.S
Henry Hallam, F.R.S
Rt. Hon. Lord Sandon, M.P.,
F.R.S.
Lieut.Col. Sykes, F.R.S
G. W. Wood, M.P., F.L.S. ...
Sir C. Lemon, Bart., M.P. ...
Lieut.  Col. Sykes, F.R.S.,
F.L.S.
Rt.Hon. the Earl Fitzwilliam
G. R. Porter, F.R.S
Travers Twiss, D.C.L.. F.R.S,
J. H, Vivian, M.P., F.R.S. ...
Rt. Hon. Lord Lyttelton
Very Rev. Dr. John Lee,
V.P.R.S.E.
Sir John P. Boileau, Bart. ...
His Grace the Archbishop of
Dublin.
James Heywood, M.P., F.R.S.
Thomas Tooke, F.R.S
R. Monckton Milnes, M.P. ...
W. Greg, Prof. Longfield.
Rev. J. E. Bromby, C. B. Fripp,.
James Heywood.
W. R. Greg, W. Langton, Dr. W. C.
Tayler.
W. Cargill, J. Heywood, W.R.Wood.
F. Clarke, R. W. Rawson, Dr. W. C.
Tayler.
C. R. Baird, Prof. Ramsay, E. W.
Rawson.
Rev. Dr. Byrth, Rev. R. Luney, R.
W. Rawson.
Rev. R. Luney, G. W. Ormerod, Dr.
W. C. Tayler.
Dr. D. Bullen, Dr. W. Cooke Tayler..
J. Fletcher, J. Heywood, Dr. Lay
cock.
J. Fletcher, Dr. W. Cooke Tayler.
J. Fletcher, F. G. P. Neison, Dr. W.
C. Tayler, Rev. T. L. Shapcott.
Rev. W. H. Cox, J. J. Danson, F. G.
P. Neison.
J. Fletcher, Capt. R. Shortrede.
Dr. Finch, Prof. Hancock, F. G. P.
Neison.
Prof. Hancock, J. Fletcher, Dr. J.
Stark.
J. Fletcher, Prof. Hancock.
Prof. Hancock, Prof. Ingram, James
MacAdam, jun.
Edward Cheshire, W. Newmarch.
B. Cheshire, J. T. Danson, Dr. W. H.
Duncan, W. Newmarch.
J. A. Campbell, E. Cheshire, W. New
march, Prof. R. H. Walsh.
SECTION F (continued). — economic science ani> statistics.
1856. Cheltenham
1857. Dublin
Rt. Hon. Lord Stanley, M.P.
His Grace the Archbishop of
Dublin, M.R.LA.
Rev. C. H. Bromby, E. Cheshire, Dr
W. N. Hancock, W. Newmarch, W
M. Tartt.
Prof. Cairns, Dr. H. D. Hutton, W..
Newmarch.
PRESIDENTS AND SECEETAEIES OF THE SECTIONS.
iv
Date and Place
Presidents
Secretaries
1858. Leeds
1859. Aberdeen...
1860. Oxford
1861. Manchester
1862. Cambridge
1863. Newcastle .
1864. Bath
1865. Birmingham
1866. Nottingham
1867. Dundee
1868. Norwich....
1869. Exeter
1870. Liverpool...
1871. Edinburgh
1872. Brighton...
187.3. Bradford ...
1874. Belfast
1875. Bristol
1876. Glasgow ...
1877. Plymouth...
1878. Dublin
1879. Sheffield ...
1880. Swansea ...
1881. York
1882. Southamp
ton.
1883. Southport
1884. Montreal ...
1885. Aberdeen...
Edward Baines
Col. Sykes, M.P., F.R.S
Nassau W. Senior, M.A
William Ne^vmarch, F.R.S... .
Edwin Chadwick, C.B
William Tite, M.P., F.R.S. ...
William Farr, M.D., D.C.L.,
F.R.S.
Rt. Hon. Lord Stanley, LL.D.,
M.P.
Prof. J. E. T. Rogers
M. E. Grant Duff, M.P
Samuel Brown, Pres. Instit.
Actuaries.
Rt . Hon. Sir Stafford H. North
cote, Bart., C.B., M.P.
Prof. W. Stanley Jevons, M.A.
Rt. Hon. Lord Neaves
Prof. Henry Fawcett, M.P. ...
Rt. Hon. W. E. Forster, M.P.
Lord O'Hagan
James Heywood, M.A., F.R.S.,
Pres.S.S.
Sir George Campbell, K.C.S.L,
M.P.
Rt. Hon. the Earl Fortescue
Prof. J. K. Ingram, LL.D.,
M.R.LA.
G. Shaw Lefevre, M.P., Pres.
S.S.
G. W. Hastings, M.P
Rt. Hon. M. E. GrantDuff,
M.A., F.R.S.
Rt. Hon. G. SclaterBooth,
M.P., F.R.S.
R. H. Inglis Palgrave, F.R.S.
Sir Richard Temple, Bart.,
G.C.S.L, CLE., F.R.G.S.
Prof. H. Sidgwick, LL.D.,
Litt.D.
T. B. Baines, Prof. Cairns, S. Brown,
Capt. Fishbourne, Dr. J. Strang.
Prof. Cairns, Edmund Macrory, A. M.
Smith, Dr. John Strang.
Edmund Macrory, W. Newmarch,
Rev. Prof. J. E. T. Rogers.
David Chadwick, Prof. R. C. Christie,
E. Macrory, Rev. Prof. J. E. T.
Rogers.
H. D. Macleod, Edmund Macrory.
T. Doubleday, Edmund Macrory
Frederick Purdy, James Potts.
E. Macrory, E, T. Payne. F. Purdy.
G. J. D. Goodman, G. J. Johnston,
E. Macrory.
R. Birkin, jun., Prof. Leone Levi, E.
Macrory.
Prof. Leone Levi, E. Macrory, A. J.
Warden.
Rev. W. C. Davie, Prof, Leone Levi.
Edmund Macrory, Frederick Purdy,
Charles T. D. Acland.
Chas. R. Dudley Baxter, E. Macrory,
J. Miles Moss.
J. G. Fitch, James Meikle.
J. G. Fitch, Barclay Phillips.
J. G. Fitch, Swire Smith.
Prof. Donnell, Frank P. Fellows,
Hans MacMordie.
F. P. Fellows, T. G. P. Hallett, B.
Macrory.
A. M'Neel Caird, T. G. P. Hallett, Dr.
W. Neilson Hancock, Dr. W. Jack.
W. F. Collier, P. Hallett, J. T. Pirn,
W. J. Hancock, C. Molloy, J. T. Pirn.
Prof. Adamson, R. E. Leader, C.
Molloy.
N. A. Humphreys, C. Molloy.
C. Molloy, W. W. Morrell, J. F.
Moss.
G. Baden Powell, Prof. H. S. Fox
well, A. Milnes, C. Molloy.
Rev. W. Cunningham, Prof. H. S.
Foxwell, J. N. Keynes, C. Molloy.
Prof. H. S. Foxwell, J. S. McLennan,
Prof. J. Watson.
Rev. W. Cunningham, Prof. H. S.
Foxwell, C. McCombie, J. P. Moss.
1836. Bristol
1837. Liverpool..
1838. Newcastle
MECHANICAL SCIENCE.
SECTION G. — MECHANICAL SCIENCE.
Davies Gilbert, D.C.L., F.R.S.
Rev. Dr. Robinson
Charles Babbage, F.R.S
T. G. Bunt, G. T. Clark, W. West.
Charles Vignoles, Thomas Webster.
R. Hawthorn, C. Vignoles, T.
Webster.
Ivi
REPORT 1885.
Date and Place
1839. Binningham
1840. Glasgow ....
1841. Plymouth
1842. Manchester
1843. Cork
1844. York
1845. Cambridge
1846. Southamp
ton.
1847. Oxford
1848. Swansea ...
1849. Birmingham
1850. Edinburgh
1851. Ipswich
1852. Belfast
1853. Hull
1854. Liverpool...
1855. Glasgow ...
1856. Cheltenham
1857. Dublin
1858. Leeds
1859. Aberdeen...
1860. Oxford
1861. Manchester
1862. Cambridge
1863. Newcastle
1864. Bath
1865. Birmingham
1866. Nottingham
1867. Dundee
1868. Norwich ...
1869. Exeter
1870. Liverpool...
1871. Edinburgh
1872. Brighton ...
1873. Bradford ...
1874. Belfast
Presidents
Prof. Willis, F.K.S., and Robt.
Stephenson.
Sir John Robinson
John Taylor, F.R.S
Rev. Prof. Willis, F.R.S
Prof. J. Macneill, M.R.LA....
John Taylor, F.R.S
George Rennie, F.R.S
Rev. Prof. Willis, M.A., F.R.S.
Rev. Prof .Walker, M.A.,F.R.S.
Rev. Prof .Walker, M.A.,F.R.S.
Robert Stephenson, M.P.,
F.R.S.
Rev. R. Robinson
William Cubitt, F.R.S
John Walker, C.E., LL.D.,
F.R.S.
William Fairbairn, C.E.,
F.R.S.
John Scott Russell, F.R.S. ...
W. J. JTacquorn Rankine,
C.E., F.R.S.
George Rennie, F.R.S
Rt. Hon. the Earl of Rosse,
F.R.S.
William Fairbairn, F.R.S. ...
Rev. Prof. Willis, M.A., F.R.S.
Prof . W. J. Macquorn Rankine,
LL.D., F.R.S.
J. F. Bateman, C.E., F.R.S....
Wm. Fairbairn, LL.D., F.R.S.
Rev. Prof. Willis, M. A., F.R.S.
J. Hawkshaw, F.R.S
Sir W. G. Armstrong, LL.D.,
F.R.S.
Thomas Hawksley, V.P.Inst.
C.E., F.G.S.
Prof.W. J. Macquorn Rankine,
LL.D., F.R.S.
G. P. Bidder, C.E., F.R.G.S.
C. W. Siemens, F.R.S
Chas. B. Vignoles, C.E., F.R.S.
Prof. Fleeming Jenkin, F.R.S.
F. J. Bramwell, C.E
W. H. Barlow, F.R.S
Prof. James Thomson, LL.D.
C.E., F.R.S.E.
Secretaries
W. Carpmael, William Hawkes, T.
Webster.
J. Scott Russell, J. Thomson, J. Tod,
C. Vignoles.
Henry Chat field, Thomas Webster.
J. F. Bateman, .J. Scott Russell, J,
Thomson, Charles Vignoles.
James Thomson, Robert Mallet.
Charles Vignoles, Thomas Webster.
Rev. W. T. Kingsley.
William Betts, jun., Charles Manby.
J. Glynn, R. A. Le Mesurier.
R. A. Le Mesurier, W. P. Struvd.
Charles Manby, W. P. Marshall.
Dr. Lees, David Stephenson.
John Head, Charles Manby.
John F. Bateman, C. B Hancock,
Cliarles Manby, James Thomson.
James Oldliam, J. Thomson, W.
Sykes Ward.
John Grantham, J. Oldham, J,
Thomson.
L. Hill, jun., William Ramsay, J.
Thomson.
C. Atherton, B. Jones, jun., H. M.
Jeffery.
Prof. Downing, W.T. Doyne, A. Tate,
James Thomson, Henry Wright.
J. C. Dennis, J. Dixon, H. Wright.
R. Abernethj", P. Le Neve Foster, H.
Wright.
P. Le Neve Foster, Rev. F. Harrison,
Henry Wright.
P. Le Neve Foster, John Robinson,
H. Wright.
W. JL Fawcett, P. Le Neve Foster.
P. Le Neve Foster, P. Westmacott,
J. F. Spencer.
P. Le Neve Foster, Robert Pitt.
P. Le Neve Foster, Henry Lea, W.
P. Marshall, Walter May.
P. Le Neve Foster, J. F. Iselin, M.
0. Tarbotton.
P. Le Neve Foster, John P. Smith,
W. W. Urquliart.
P. Le Neve Foster, J. F. Iselin, C.
Manby, W. Smith.
P. Le Neve Foster, H. Bauerman.
H. Bauerman, P. Le Neve Foster, T.
King, J. N. Shoolbred.
H. Bauerman, Alexander Leslie, J.
P. Smith.
H. M. Brunei, P. Le Neve Foster,
J. G. Gamble, J. N. Shoolbred.
Crawford Barlow, H. Bauerman,
E. H. Carbutt, J. C. Hawkshaw,
J. N. Shoolbred.
A. T. Atchison, J. N. Shoolbred, John
Smyth, jun.
PRESIDENTS AND SECRETARIES OF THE SECTIONS.
Ivii
Date and Place
1875. Bristol
1876. Glasgow ..
1877. Pljmouth..
1878. Dublin
1879. Sheffield ..
1880. Swansea ..
1881. York
Presidents
Secretaries
1882. Southamp
ton.
1883. Southport
1884. Montreal ..
1885. Aberdeen..
W. Froude, C.E., M.A., F.R.S.
C. W. Merrifield, F.R.S
Edward Woods, C.E
Edward Easton, C.E
J. Robinson, Pres. Inst. Mech.
Eng.
James Abernethy, V.P.Inst.
O.E., F.R.S.E.
Sir W. G. Armstrong, C.B.,
LL.D., D.C.L., F.R.S.
John Fowler, C.E., F.G.S. ...
James Brunlees, F.R.S.E.,
Pres.Inst.C.E.
Sir F. J. Bramwell, F.R.S.,
V.I'.Inst.C.E.
B. Baker, M.Inst.C.E
W. R. Browne, H. M. Brimel, J. G.
Gamble, J. N. Shoolbred.
W. Bottomlev, jun., W. J. Millar,
J. N. Shoolbred, J. P. Smith.
A. T. Atchison, Dr. Merrifield, J. N.
Shoolbred.
A. T. Atchison, R. G. Symes, H. T.
Wood.
A. T. Atchison, Emerson Bainbridge,
H. T. Wood.
A. T. Atchison, H. T. Wood.
A. T. Atchison, J. F. Stephenson,
H. T. Wood.
A. i'. Atchison, F. Ghurton, H. T.
Wood.
A. T. Atchison, E. Rigg, H. T. Wood.
A. T. Atchison, W. B. Dawson, J.
Kennedy, H. T. Wood.
A. T. Atchison, F. G. Ogilvie, E.
Rigg, J. N. Shoolbred.
ANTHROPOLOGICAL SCIENCE.
1884. Montreal..
1885. Aberdeen..
SECTION H. — ANTHROPOLOGY.
E. B. Tylor, D.C.L., F.R.S. ...
Francis Galton, MA., F.R.S.
G. W. Bloxam, W. Hurst.
G. W. Bloxam, Dr. J. G. Garson, W.
Hurst, Dr. A. Macgregor.
LIST OF EVENING LECTURES.
Date and Place
1842. Manchester
J1843. Cork
1844. York ,
1845. Cambridge
1846. Southamp
ton,
1847. Oxford.
Lecturer
Charles Vignoles, F.R.S. .
Sir M. I. Brunei
R. I. Murchison
Prof. Owen, M.D., F.R.S...
Prof. E. Forbes, F.R.S
Dr. Robinson
Charles Lyell, F.R.S
Dr. Falconer, F.R.S
G.B.Airy,F.R.S.,Astron.Royal
R. I. Murchison, F.R.S
Prof. Owen, M.D., F.R.S. ...
Charles Lyell, F.R.S
W. R. Grove, F.R.S
Rev. Prof. B. Powell, F.R.S.
Prof. M. Faraday, F.R.S
Hugh E. Strickland, F.G.S... .
Subject of Discourse
The Principles and Construction of
Atmospheric Railways,
The Thames Tunnel.
The Geology of Russia.
The Dinornis of New Zealand.
The Distribution of Animal Life in
the ^gean Sea.
The Earl of Rosse's Telescope.
Geology of North America.
The Gigantic Tortoise of the Siwalik
Hills in India.
Progress of Terrestrial Magnetism.
Geology of Russia.
Fossil Mammalia of the British Isles.
Valley and Delta of the Mississippi.
Properties of the Explosive substance
discovered by Dr. Schonbein ; also
some Researches of his own on the
Decomposition of Water by Heat.
Shooting Stars.
Magnetic and Diamagnetic Pheno
mena.
The Dodo {Bidus ineptus).
Iviii
REPORT 1885.
Date and Place
1848. Swansea ,
1849. Birmingham
1850. Edinburgh
1851. Ipswich ..
1852. Belfast
1853, Hull.
1854. Liverpool...
1855. Glasgow ...
1856. Cheltenham
Lecturer
1857. Dublin....
1858. Leeds ....
1859. Aberdeen.
1860. Oxford
1861. Manchester
1862. Cambridge
1863. Newcastle
1864. Bath
1865. Birmingham
1866. Nottingham
John Percy, M.D., F.R.S
W. Carpenter, M.D., F.R.S... .
Dr. Faraday, F.K.S
Rev. Prof. Willis, M.A., F.R.S.
Prof. J. H. Bennett, M.D.,
F.R.S.E.
Dr. Mantell, F.R.S
Prof. R. Owen, M.D., F.R.S.
G.B.Airy,F.R.S.,Astron. Royal
Prof. G. G. Stokes, D.C.L.,
F.R.S.
Colonel Portlock, R.E., F.R.S.
Prof. J. Phillips, LL.D., F.R.S.,
F.G.S.
Robert Hunt, F.R.S
Prof. R. Owen, M.D., F.R.S.
Col. E. Sabine, V.P.R.S
Dr. W. B. Carpenter, F.R.S.
Lieut.Col. H. Rawlinson ...
Col. Sir H. Rawlinson
W. R. Grove, F.R.S
Prof. W. Thomson, F.R.S. ...
Rev. Dr. Livingstone, D.C.L.
Prof. J. Phillips,LL.D.,F.R.S.
Prof. R. Owen, M.D., F.R.S.
Sir R. I. Murchison, D.C.L... .
Rev. Dr. Robinson, F.R.S. ...
Rev. Prof. Walker, F.R.S. ...
Captain Sherard Osborn, R.N.
Prof. W. A. Miller, M.A., F.R.S.
G.B.Airy,F.R.S.,Astron.Royal
Prof. Tyndall, LL.D., F.R.S.
Prof. Odliug, F.R.S
Prof. Williamson, F.R.S
James Glaisher, F.R.S.,
Prof. Roscoe, F.R.S
Dr. Livingstone, F.R.S.
J. Beete Jukes, F.R.S. ..
William Huggins, F.R.S. ...
Dr. J. D. Hooker, F.R.S
Subject of Discourse
Metallurgical Operations of Swansea
and its neighbourhood.
Recent Microscopical Discoveries.
Mr. Gassiot's Battery.
Transit of diiferent Weights with
varying velocities on Railways.
Passage of tlie Blood through the
minute vessels of Animals in con
nexion with Nutrition.
Extinct Birds of New Zealand.
Disi inct ion between Plants and Ani
mals, and tlieir changes of Form.
Total Solar Eclipse of July 28, 1851.
Recent discoveries intlie properties
of Light.
Recent discovery of Rocksalt at
Carrickfergus, and geological and
pract ical considerations connected
with it.
Some peculiar Phenomena in the
Geohigy and Physical Geography
of Yorkshire.
The present state of Photography.
Anthropomorphous Apes.
Progress of researches in Terrestrial
Magnetism.
Characters of Species.
Ass3Tian and P>abylonian Antiquities
and Etlinology.
Recent Discoveries in Assyi'ia and
Babylonia, v^^ith the results of
Cuneiform research up to the
present time.
Correlation of Plij'sical Forces.
The Atlantic Telegraph.
Recent Discoveries in Africa.
The Ironstones of Yorkshire.
The Fossil Mammalia of Australia.
Geology of the Nortliern Highlands.
Electrical Discharges in highly
rarefied Media.
Physical Constitution of the Sun.
Arctic Discovery.
Spectrum Analysis.
The late Eclipse of the Sun.
The Forms and Action of Water.
Organic Chemistry.
The Chemistry of the Galvanic Bal
tery considered in relation to
Dynamics.
The Balloon Ascents made for the
British Association.
The Chemical Action of Light.
Recent Travels in Africa.
Probabilities as to the position and
extent of the Coalmeasures be
neath the red rocks of the Mid
land Counties.
The results of Spectrum Analysis
applied to Heavenly Bodies.
Insular Floras.
LIST OF EVENING LECTDBES.
lis
Date and Place
1867. Dundee.
1868. Norwich ...
1869. Exeter
1870. Liverpool...
1871. Edinburgh
1872. Brighton ...
1873. Bradford ...
1874. Belfast
1876. Bristol
1876. Glasgow ...
1877. Plymouth .
1878. Dublin
1879. Sheffield ...
1880. Swansea ...
1881. York.
1882. Southamp
ton.
1883. Southport
1884. Montreal...
1885. Aberdeen..
Lecturer
Archibald Geikie, F.R.S
Alexander Herschel, F.R.A.S.
J. Fergiisson, F.E.S
Dr. W. Odling, F.R.S
Prof. J. Phillips, LL.D.,F.E.S.
J. Norman Lockyer, F.R.S....
Prof. J. Tyndall, LL.D., F.R.S.
Prof .W. J. Macquorn Eankine,
LL.D., F.R.S.
F. A. Abel, F.R.S
E. B. Tylor, F.R.S
Prof. P.Martin Duncan, M.B.,
TCI T> Q
Prof. W.K. Clifford
Subject of Discourse
Prof. W. C.Williamson, F.R.S.
Prof. Clerk Maxwell, F.R.S.
Sir John Lubbock,Bart.,M.P.,
F.R.S.
Prof. Huxley, F.R.S
■W.Spottiswoode,LL.D.,F.R.S.
F. J. Bramwell, F.R.S
Prof. Tait, F.R.S.E
SirAVyville Thomson, F.R.S.
W. Warington Smyth, M.A.,
F.R.S.
Prof. Odling, F.R.S
G. J. Romanes, F.L.S
Prof. Dewar, F.R.S
W. Crookes, F.R.S
Prof. E. Ray Lankester, F.R.S.
Prof. W. Boyd Dawkins,
F.R.S.
Francis Galton, F.R.S
Prof. Huxley, Sec. R.S
W. Spottiswoode, Press. R.S.
Prof. Sir Wm. Thomson, F.R.S.
Prof. H. N. Moseley, F.R.S.
Prof. R. S. Ball, F.R.S
Prof. J. G. McKendrick,
F.R.S.E.
Prof. O. J. Lodge, D.Sc
Rev. W. H. DaUinger, F.R.S.
Prof. W. G. Adams, F.R.S. ..,
John Murray, F.R.S.E
The Geological Origin of the present
Scenery of Scotland.
The present state of knowledge re
garding Meteors and Meteorites.
Archeology of the early Buddhist
Monuments.
Reverse Chemical Actions.
Vesuvius.
The Physical Constitution of the
Stars and Nebulse.
The Scientific Useof the Imagination.
Streamlines and Waves, in connec
tion with Naval Architecture.
Some recent investigations and ap
plications of Explosive Agents.
The Relation of Primitive to Modern
Civilization.
Insect Metamorphosis.
The Aims and Instruments of Scien
tific Thouglit.
Coal and Coal Plants.
Molecules.
Common Wild Flowers considered
in relation to Insects.
The Hypothesis that Animals are
Automata, and its History.
Tlie Colours of Polarized Light.
Railway Safety Appliances.
Force.
The Cliallfngcr Expedition.
The Physical Phenomena connected
with the Mines of Cornwall and
Devon.
The new Element, Gallium.
Animal Intelligence.
Dissociation, or Modern Ideas of
Chemical Action.
Radiant Matter.
Degeneration.
Primeval Man.
Mental Imagery.
The Rise and Progress of Palason*
tology.
The Electric Discharge, its Forms
and its Functions.
Tides.
Pelagic Life.
Recent Researches on the Distance
of the Sun.
Galvani and Animal Electricity.
Dust.
The Modern Microscope in Re
searches on the Least and Lowest
Forms of Life.
The Electric Light and Atmospheric
Absorption.
The Great Ocean Basins.
Ix
REPORT — 1885.
LECTURES TO THE OPERATIVE CLASSES.
Date and Place
Lecturer
Subject of Discourse
1867. Dundee
Prof. J. Tyndall, LL.D.,F.K.S.
Matter and Force.
1868. Norwich ...
Prof. Huxley, LL.D., F.E.S.
A Piece of Chalk.
1869. Exeter
Prof. Miller, M.D., F.E.S. ...
Experimental illustrations of the
modes of detecting the Composi
tion of the Sun and other Heavenly
Bodies by the Spectrum.
1870. Liverpool...
Sir John Lubbock, Bart.,M.P.,
F.K.S.
Savages.
1872. Brighton ...
W.Spottiswoode,LL.D.,F.R.S.
Sunshine, Sea, and Sky.
1873. Bradford ...
C. W. Siemens, D.C.L., F.R.S.
Fuel.
1 874 Belfast
Prof Odlino. F.R.S
The Discovery of Oxygen,
A Piece of Limestone.
X O 1 ^ t ^ v7 i. J. CuO Li ■•((•*
1875. Bristol
Dr. W. B. Carpenter, F.R.S.
1876. Glasgow ...
Commander Cameron, C.B.,
R.N.
W. H. Preece
A Journey through Africa.
1877. Plymouth...
1879 Sheffield
Telegraphy and the Telephone.
Electricity as a Motive Power.
The NorthEast Passage.
W E Avrton
1880. Swansea ...
H. Seebohm, F.Z.S
1881. York
Prof. Osborne Reynolds,
Raindrops, Hailstones, and Snow
F.R.S.
flakes.
1882. Southamp
John Evans, D.C.L. Treas. R.S.
Unwritten History, and how to
ton.
read it.
1883. Southport
Sir F. J. Bramwell, F.R.S. ...
Talking by Electricity — Telephones.
1884. Montreal ...
Prof. R.S. Ball, F.R.S
Comets.
1885. Aberdeen...
H. B. Dixon, M.A
The Nature of Explosions.
Ixi
OFFICERS OF SECTIONAL COMMITTEES PRESENT AT THE.
ABERDEEN MEETING.
SECTION A. — MATHEMATICAL AND PHYSICAL SCIENCE.
Fresiclent.—FToiessor G. Chrystal, M.A., F.R.S.E.
VicePresidents.— ProkssoT C. Niven, F.R.S. ; Lord Rayleigh, F.R.S. ;.
Professor A. Schuster, F.R.S. ; Professor G, G. Stokes, Sec.R.S. ;
Professor Sir W. Thomson, F.R.S.
Secretaries— R. E. Baynes, M.A. ; R. T. Glazebrook, F.R.S. ; Professor
W. M. Hicks, F.R.S. (Becorder) ; Professor W. Ingram, M.A.
SECTION B. — CHEMICAL SCIENCE.
President.— Proiessov H. E. Armstrong, Ph.D., F.R.S., Sec.C.S.
VicePresidents. — Professor Brazier, F.C.S. ; Professor A. Crum Brown,
F.R.S. ; Professor Hartley, F.R.S. ; Professor H. McLeod, F.R.S. ;
Professor W. A. Tilden, F.R.S.
Secretaries. — Professor P. Phillips Bedson, D.Sc. {Becorder) ; H. B.
Dixon, M.A. ; H. Forster Morley, D.Sc. ; W. J. Simpson, M.D.
SECTION C. — GEOLOGY.
PrmcZen^.— Professor J. W. Jndd, F.R.S., Sec.G.S.
VicePresidents. — John Evans, Treas.R.S.; Rev. George Gordon, LL.D, ;
T. F. Jamieson, LL.D. ; Rev. J. M. Joass, LL.D. ; Professor O. C.
Marsh, M.A. ; Professor W. C. Williamson, F.R.S.
Secretaries.— C. E. De Ranee, F.G.S. ; J. Home, F.R.S.E. ; J. J. H.
Teall, F.G.S. ; W. Topley, F.G.S. {Recorder).
SECTION D. — BIOLOGY.
President.— PTo^esaov W. C. Mcintosh, M.D., LL.D., F.R.S. L. and E.,
F.L.S.
VicePresidents. — Professor C. C. Babington, F.R.S. ; Professor I. Bayley
Balfonr, F.R.S. ; Professor Cleland, F.R.S. ; Sir John Lubbock,
Bart., F.R.S.; Professor J. S. Bnrdon Sanderson, F.R.S.; Pro
fessor W. Stirling, F.R.S.E. ; Professor Trail, F.L.S.
Secretaries. — W. Heape ; J. McGiegor Robertson, M.B. ; J. Duncan
Matthews, F.R.S.E. ; Howard Saunders, F.L.S. {Recorder) ; H..
Marshall Ward, M.A.
Ixii REPORT — 1885.
SECTION E. — GEOGRAPHY.
Fresident.— General J. T. Walker, C.B., R.E., LL.D., F.R.S.
VicePresidents. — Professor James Donaldson, F.R.S.E. ; Admiral Sir E.
Ommanney, C.B,, F.R.S. ; Lieat. Colonel R. L. Playfair; Dr. John
Rae, F.R.S.
Secretaries.— J. S. Keltie ; J. S. O'Halloran, F.R.G.S.; E. G. Raven
stein, F.R.G.S. (Recorder) ; Rev. G. A. Smith, M.A.
SECTION F. — ECONOMIC SCIENCE AND STATISTICS.
President. — Professor Henry Sidgwick, LL.D., Litt.D.
VicePresidents. — Professor Adanison, LL.D. ; Dr. Alexander Bain ;
Major P. G. Craigie ; Sir Richard Temple, Bart., G.C.S.I.
.Secretaries. — Rev. W. Cunningham, B.D. ; Professor H. S. Foxwell,
M.A. (Recorder) ; C. McCombie ; J. F. Moss.
SECTION G. — MECHANICAL SCIENCE.
President. — Benjamin Baker, M.Inst. C.E.
VicePresidents. — W. H. Barlow, F.R.S. ; Sir James N. Douglass ; Pro
fessor James Thomson, F.R.S. ; Professor W. C. Unvvin.
■Secretaries. — A. T. Atchison, M.A. ; F. G. Ogilvie, M.A., B.Sc. ; E.
Rigg, M.A. (Recorder) ; J. N. Shoolbred, B.A.
SECTION H. — ANTHROPOLOGY.
President. — Francis Galton, M.A., F.R.S., President of the Anthropo
logical Institute.
VicePresidents. — Dr. Alexander Bain ; Professor D. J. Cunningham,
M.D. ; Professor Flower, F.R.S. ; W. Pengelly, F.R.S. ; Professor
Strnthers, M.D. ; Professor W. Turner, F.R.S.
.Secretaries. — G. W. Bloxam, F.L.S. (Recorder) ; J. G. Garson, M.D. ;
Walter Hurst, B.Sc. ; A. McGregor, M.D.
Eh
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Ixiv
EEPORT — 1885.
Ta^le showing the AttendaTice and ReceipU
Date of Meeting
1831, Sept. 27 ..
1832, June 19 ..
1833, June 25 ..
1834, Sept. 8 ..
1835, Aug. 10 ..
1836, Aug. 22 ..
1837, Sept. 11 ..
1838, Aug. 10 ..
183!), Aug. 26 ..,
1840, Sept. 17 ..
1841, July 20 ..
1842, June 23 ..
1843, Aug. 17 ..
1844, Sept. 26 ..
1845, June 19 ..
1846, Sept. 10 ..
1847, June 23 ..
1848, Aug. 9 ..
1849, Sept. 12 ..
1850, July 21 ..
1851, July 2 ..
1852, Sept. 1 ..
1853, Sept. 3 ..
1854, Sept. 20 ..
1855, Sept. 12 ..
1856, Aug. 6 ..
1857, Aug. 26 ..
1858, Sept. 22 ..
1859, Sept. 14 ..
1860, June 27 ..
1861, Sept. 4 ..
1862, Oct. 1 ..
1863, Aug. 26 ..
1864, Sept. 13 ..
1865, Sept. 6 ..
1866, Aug. 22 ..
1867, Sept. 4 ..
1868, Aug. 19 ..
1869, Aug. 18 ..
1870, Sept. 14 ..
1871, Aug. 2 .,
1872, Aug. 14 ..
1873, Sept. 17 .,
1874, Aug. 19 .
1875, Aug. 25 .
1876, Sept. 6 .
1877, Aug. 15 .
1878, Aug. 14 .
1879, Aug. 20 .
1880, Aug. 25 .
1881, Aug. 31 .
] 882, Aug. 23 .
1883, Sept. 19 .,
1884, Aug. 27 .
1885, Sept. 9 .
Where held
Presidents
York
Oxford
Cambridge
Edinburgh
Dublin
Bristol
Liverpool
NewcastleonTyne
B irmingham
Glasgow
PljTnoiith
Manchester
Cork
York
Cambridge
Southamijton
Oxford
Swansea
Birmingham
Edinburgh
Ipswich
Belfast
Hull
Liverpool
Glasgow
Cheltenham
Dublin
Leeds
Aberdeen
Oxford
Manchester
Cambridge
NewcastleonTyne
Bath
Birmingham
Nottingham
Dundee
Norwich
Exeter
Liverpool
Edinburgh
Brighton
Bradford
! Belfast
! Bristol
Glasgow
Plymouth
Dublin
Sheffield
Swansea
York
Southampton
Southport
Montreal
Aberdeen
The Earl Fitzwilliam, D.C.L.
The Rev. W. Buckland, F.R.S.
The Rev. A. Sedgwick, F.R.S.
Sir T. M. Brisbane, D.C.L
The Rev. Provost Lloyd, LL.D.
The Marquis of Lansdowne ...
The Earl of Burlington, F.R.S.
The Duke of Northumberland
The Rev. W. Vernon Harcourt
The Marquis of Breadalbane...
The Rev. W. WnevfeU, F.R.S.
The Lord Francis Egertou
The Earl of Rosse, F.R.S
The Rev. G. Peacock, D.D. ...
Sir John F. W. Herschel, Bart.
Sir Roderick I. i\Iurchison,Bart.
Sir Robert H. Inglia, Bart
The Marquis of Northampton
The Rev. T. R. Robinson, D.D.
Sir David Brewster, K.H
G. B. Airy, Astronomer Royal
Lieut.General Saljine, F.R.S.
William Hopkins, F.R.S
The Earl of Harrowby, F.R.S.
The Duke of Arayll, F.R.S. ...
Prof. C. G. B. Daubeny, M.D.
The Rev.Humphiev Lloyd, D.D.
Richard Owen, M'D., D.C.L....
H.R.H. the Prince Consort ...
I The Lord Wrottesley, M.A. ..
WilliamFairbaim,LL.D.,F.R.S.
I The Rev. Prof essor Willis, M.A.
Sir William G.Armstrong, C.B.
Sir Charles Lyell, Bart., M.A.
1 Prof. J. Phillips, M.A., LL.D.
I William R. Grove, Q.C., F.R.S.
I The Duke of Buccleuch,K.C.B.
1 Dr. Joseph D. Hooker, F.R.S.
i Prof. G. G. Stokes, D.C.L
Prof. T. H. Huxley, LL.D
Prof. Sir W. Thomson, LL.D.
Dr. W. B. Carpenter, F.R.S. ...
Prof. A. W. Williamson, F.R.S.
Prof. J. Tyndall, LL.D., F.R.S.
SirJohnHawkshaw,C.E.,F.R.S.
Prof. T. Andrews, M.D., F.R.S.
Prof. A. Thomson, M.D., F.R.S.
W. Spottiswoode, M.A., F.R.S.
Prof.G. J. Allman, M.D., F.R.S.
A. C. Ramsay, LL.D., F.R.S....
Sir John Lubbock, Bart., F.R.S.
Dr. C. W. Siemens, F.R.S
Prof. A. Cayley, D.C.L., F.R.S.
Prof. Lord Rayleigh, F.R.S. ...
Sir Lyon Playf air, K.C.B.,F.E.S.
Old Life
Members
169
303
109
226
313
241
314
149
227
235
172
164
141
238
194
182
236
222
184
286
321
239
203
287
292
207
167
196
204
314
246
245
212
162
239
221
173
201
184
144
272
178
203
235
225
ATTENDANCE AND RECEIPTS AT ANNUAL MEETINGS.
Ixv
Innual Meetings of the Association.
Attended by
Amount
Sums paid on
Account of
Grants for
Scientific
Purposes
Old
anual
mbers
New
Annual
Members
Asso
ciates
Ladies
For
eigners
Total
received
during the
Meeting
Year
...
...
...
353
1831
1832
...
...
...
...
900
1298
1833
18.34
1835
£20
167
•••
...
lioo*
...
1350
1840
2400
435
922 12 6
932 2 2
1836
1837
1838
46
ill
376
185
190
22
39
40
25
"eo*
331*
160
260
172
196
203
197
34
40
28
35
36
53
15
1438
1353
891
1315
1079
857
1320
819
1595 11
1546 16 4
1235 10 11
1449 17 8
1565 10 2
981 12 8
831 9 9
685 16
208 5 4
275 1 8
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
75
'33t
'"at
407
270
495
376
71
45
94
65
197
54
£m"6'o
93
33
447
237
22
1071
963
159 19 6
1849
128
42
510
273
44
1241
1085
345 18
1850
61
47
244
141
37
710
620
391 9 7
1851
63
60
510
292
9
1108
1085
304 6 7
1852
56
57
367
236
6
876
903
205
1853
121
121
76.5
524
10
1802
1882
380 19 7
1854
142
101
1094
543
26
2133
2311
480 16 4
1855
104
48
412
346
9
1115
1098
734 13 9
1856
156
120
900
569
26
2022
2015
507 15 4
1857
111
91
710
509
13
1698
1931
618 18 2
1858
125
179
1206
821
22
2564
2782
684 11 1
1859
177
59
636
463
47
1689
1604
766 19 6
1860
184
125
1589
791
15
3138
3944
1111 5 10
1861
150
57
433
242
25
1161
1089
1293 16 6
1862
154
209
1704
1004
25
3335
3640
1608 3 10
1863
182
103
1119
1058
13
2802
2965
1289 15 8
1864
215
149
766
508
23
1997
2227
1591 7 10
1865
J18
105
960
771
11
2303
2469
1750 13 4
1866
193
118
1163
771
7
2444
2613
1739 4
1867
J26
117
720
682
45
2004
2042
1940
1868
229
107
678
600
17
1856
1931
1622
1869
503
195
1103
910
14
2878
3096
1572
1870
511
127
976
754
21
2463
2575
1472 2 6
1871
280
80
937
912
43
2533
2649
1285
1872
237
99
796
601
11
1983
2120
1685
1873
532
85
817
630
12
1951
1979
1151 16
1874
307
93
884
672
17
2248
2397
960
1875
531
185
1265
712
25
2774
3023
1092 4 2
1876
238
59
446
283
11
1229
1268
1128 9 7
1877
290
93
1285
674
17
2578
2615
725 16 6
1878
239
74
629
349
13
1404
1425
1080 11 11
1879
171
41
889
147
12
915
899
731 7 7
1880
U13
176
1230
514
24
2557
2689
476 3 1
1881
253
79
516
189
21
1253
1286
1126 1 11
1882
!30
323
952
841
5
2714
3369
1083 3 3
1883
517
219
826
74
26&60H.§
1777
1538
1173 4
1884
532
122
1053
447
6
2203
2256
1385
1885
dies were not admitted ty purchased Tickets until 1843. + Tickets of Admission to Sections only,
cludmg Ladies. § Fellows of the American Association wer» admitted as Honorary Members for this Meeting
d
OFFICERS AND COUNCIL, 188586.
PRESIDENT.
The Right Hon. SIR LYON PLATFAIR, K.C.B., M.P., Ph.D., LL.D., F.R.S.L.&E., F.C.S.
VICEPRESIDENTS.
His Grace the Duke o£ Richmond and Gordon, K.G., D.C.L., Cliaucellor of tlie
University of Aberdeen.
Tlie Right Hon. the Earl of Aberdeen, LL.D., LordLieutenant of Aberdeenshire.
The Right Hon. the Earl of Crawkord and Balcarres, M.A., LL.D., F.R.S., F.R.A.S.
James Matthews, Esq., Lord Provost of the City of Aberdeen.
Professor Sir William Thomson, M.A., LL.D., F.R.S. L. & E., F.R.A.S.
Alexander B.un, Esq., M.A., LL.D.. Rector of the University of Aberdeen.
Professor W. H. Flower, LL.D., F.R.S., F.L.S., F.G.S., Pres. Z.S., Director of
the Natural History Museum, London.
Professor John Struthers, M.D., LL.D.
PRESIDENT ELECT.
Sir William Dawson, C.M.G., JI.A.. LL.D., F.R.S. , P.G.S., Principal of McGill College, Montreal, Canada.
VICEPRESID
The Right Hon. the Earl op Bradford, Lord
Lieutenant of Shropsliire.
The Riglit Hon. Lord Leioh, D.C.L., LordLieu
tenant of Warwicksiiire.
The Bight Hon. LoiiD Norton, K.C.M.G.
The Right Hon. Loud Wrottesley, LordLieu
tenant of Staffordshire.
ENTS ELECT.
The Riglit Rev. the Lord Bishop of Worcester,
D.D.
THOJU.S Martineau, Esq., Mayor of Birmingham.
Professor G. G. Stokes, D.C.L., LL.D., Pres. R.S.
Professor W. A. Tilden, D.Sc, F.R.S., F.C.S.
Rev. A. R. Vardy, M.A.
Rev. A. W. Watson, D.Sc, F.R.S.
LOCAL SECRETARIES FOR THE MEETING AT BIRMINGHAM.
J. BarhUI Carslake, Esq.  Rev. H. W. Crosskey, LL.D., F.G.S.  Charles J. Hart, Esq.
LOCAL TREASURER FOR THE MEETING AT BIRMINGHAM.
J. D. Goodman, Esq.
ORDINARY MEMBERS
Abney. Capt. W. DE W., F.R.S.
Ball, Professor R. S., F.R.S.
Bateman, J. F. La Trobe. Esq., F.R.S.
BL.4.NF0RD, W. T., Esq., F.R.S.
Bramwell, Sir F. J.. F.R.S.
Crookes, W., Esq., F.R.S.
Dawkins, Professor W. Boyn, F.R.S.
De La Rue, Dr. Warren, F.R.S.
Dewar, Professor J., F.R.S.
Flower, Professor W. H., F.R.S.
Gl.\dstoxe, Dr. J. H., F.R.S.
Gl.u.sheb, J. W. L., Esq., F.R.S.
God WIN Austen, Lieut.Col. H. H., F.R.S.
OF THE COUNCIL.
Hawkshaw, J. Clarke, Esq., F.G.S.
Hknrici, Professor 0., F.R.S.
Hughes, Professor T. McK., F.G.S.
Martin, J. B., Esq.. F.S.S.
M'Leod, Professor H., F.R.S.
MosKLEV. Professor H. N., F.R.S.
Ojimanxey, Admiral Sir E., C.B., F.R.S.
Pengelly, W., Esq., F.R.S.
Perkin, Dr. W. H., F.R.S.
SORBY, Dr. H. C. F.R.S.
Temple, Sir R., Bart. G.C.S.I.
ThiseltonDyer, W. T., Esq., C.M.G.,
F.B.S.
GENERAL SECRETARIES.
Capt. Douglas Galton, C.B., D.C.L., LL.D., F.R.S., F.G.S., 12 Chester Street, London, S.\7.
A. G. Vernon Harcourt, Esq., M.A., LL.D., F.R.S., F.C.S., Cowley Grange. Oxford.
SECRETARY.
Arthur T. Atchison, Esq., M.A., 22 Albemarle Street, London, W.
GENERAL TREASURER.
Professor A. W. Williamson, Ph.D., LL.D., F.R.S., F.C.S., University College, London, W.C.
EXOFFICIO MEMBERS OF THE COUNCIL.
The Trustees, the President and President Elect, tlie Presiilents of former years, the VicePresidents and
VicePresidents Elect, the General and Assistant General Secretaries for the present and former yeais,
the Secretary, the Genpral Treasurers for the present and former years, and the Local Treasurer and
Secretaries for the eusuuig Meeting.
TRUSTEES (PERMANENT).
Sir John Lubbock, Bart.. MP., D.C.L., LL.D., F.R.S., Pres. L.S.
The Right Hon. Lord Rayleigh, M.A., D.C.L., LL.D., Sec. R.S., F.R.A.S.
The Right Hon. Sir Lyon Playfair, K.C.B., M.P., Ph.D., LL.D., F.R.S.
PRESIDENTS OF FORMER TEARS.
The Duke of Devonshire, K.G.
Sir G. B. Airy, K.C.B., F.R.S.
The Duke of Argyll, K.G., K.T.
Sir Richard Owen, K.C.B., F.R.S.
Sir W. G. Armstrong, C.B., LL.D.
Sir William R. Grove, F.R.S.
Sir Joseph D. Hooker, K.C.S.I.
Prof. Stokes, D.C.L., Pres. R.S.
Prof. Huxley, LL.D., F.R.S.
Prof. Sir Wm. Tliomson, LL.D.
Prof. Williamson, Ph.D., F.R.S.
Prof. Tvndall, D.C.L., F.R.S.
Sir John Hawkshaw, F.R.S.
Prof. AUman, M.D., F.R.S.
Su A. C. Ramsay, LL.D., F.R.S.
Sir John Lubbock, Bart., F.R.S.
Prof, Cayley, LL.D., F.R.S.
Lord Rayleigh, D.C.L., Sec. R.S.
P. Galton. Esq., F.R.S.
Dr.T. A. Hirst, F.R.S.
GENERAL OFFICERS OP FORMER TEARS.
I Dr. Michael Foster, Sec. R.S.  P. L. Sclater, Esq., Ph.p.,_P.R.S. ,
GeorgeGriffith, Esq., M.A,, F.C.S. I Prof. Bonney, D.Sc, F.R.S.
John Evans, Esq., D.C.L., F.R.S.
AUDITORS.
I W. Huggins, Esq., D.C.L.,
F.R.S. I W. H. Preece, Esq., F.R.S.
Ixvii
REPORT OF THE COUNCIL.
Heport of the Council for the year 188485, presented to the General
Committee at Aberdeen, on Wednesday, September 9, 1885.
The Council have received reports during the past year from the
Oeneral Treasurer, and his accounts for the year will be laid before the
General Committee this day.
Since the Meeting at Montreal, the following have been elected
Corresponding Members of the Association : —
Bowditch, Prof. H. P. Kikuchi, Prof. Dairoku.
Brusb, Prof. G. J. Michelson, A. A.
Gibbs, Prof. J. Willard. Newcomb, Prof. Simon.
Gibbs, Prof. Wolcott. Powell, Major J. W.
Greely, Lieut. A. W. Ray, Captain P. H.
Jackson, Prof. C. Loring. Thurston, Prof. R. H.
The Council have nominated Professor Struthers, M.D., LL.D., to
he a VicePresident at the Meeting at Aberdeen.
Soon after the commencement of the present year, Professor Bonney,
the Secretary, informed the Council that a considerable increase in the
endowment of his Professorship at University College would demand
that in future a larger share of his time should be devoted to teaching.
As unfortunately the state of his health for some months past had pointed
to the need of diminishing rather than increasing his work, he regretted
that he would be unable to offer himself for reelection at the present
Meeting. The Council received this announcement with very great
regret." Professor Bonney not only brought to the office of Secretary a
leading scientific position, but also combined with this advantage great
energy, zeal, and discretion. It was largely due to his powers of organi
sation and tact that the exceptional and grave difficulties which attended
the holding of last year's Meeting at Montreal were surmounted, and it
was brought to a successful issue. The Council have nominated Mr. A. T.
Atchison M.A., who for some years past has rendered most efficient
assistance as one of the Secretaries of Section G, to the office of Secretary,
vacated by Professor Bonney.
During the present year the Council have considered the stipend
paid to Mr. Stewardson, the Clerk of the Association, and the amount
assigned to the General Treasurer to enable him to obtain such assistance
as may be requisite. Mr. Stewardson was engaged in the year 1873 at a
salary of 120Z., which was subsequently augmented to VSOl. The Council
now recommend that for the present year it be raised to 135Z., and be
subsequently increased (subject to the usual conditions) by a sum of 51. at
the end of each three years till a maximum of 160L be reached ; also that
the yearly sum assigned to the General Treasurer be increased from 501.
to 601.
d 2
Ixviii KEPORT — 1885.
On meeting again in Great Britain, the Council venture to express
to the General Committee their belief that the anticipations of a successful
meeting, expressed in the Report presented at Montreal, have been fully
justified by the results, and once more give utterance to the gratitude,
which must be felt by all who visited Canada, for the liberal hospitality
and cordial reception which welcomed them there. It will be long before
this visit is forgotten, or the stimulus, which its exceptional circumstances
gave to the energy and life of the Association, ceases to be felt. Towards
the close of that Meeting the happy idea occurred to several members of
the Association that it would be an appropriate memorial of the visit
of the British Association to found a Medal at McGill University, to be
given annually for proficiency in Applied Science. The idea, once started,
was warmly espoused, and a subscription list was opened, with Lord
Rayleigh, the President, as Treasurer, and Messrs. W. Topley and H. T.
Wood as Secretaries. The result has been that a sum of about 5001.
will be transmitted to the authorities of the McGill University for invest
ment. This will enable them to offer, as an annual prize, a Gold Medal
and a sum of money. The first award has already been made. The
Council, acting under the powers conferred upon them by the General
Committee on Nov. 11, 1884, have instructed Mr. Wyon to prepare, at
the cost of the Association, a suitable die for the Medal.
The Council, in virtue of the powers conferred upon them by the
General Committee at Montreal, in regard to the report concerning
Corresponding Societies, have formed the Corresponding Societies'
Committee. The Report of the Committee will be presented, and a con
ference of Delegates, appointed under the new rules, will be held during
the present meeting.
The following resolutions were referred by the General Committee to
the Council for consideration and action, if desirable : —
' That the Council of the Association be requested to communicate
with the Government of the Dominion of Canada in order (1) to call
the attention of the Government to the absence of trustworthy informa
tion concerning the tides of the Gulf of St. Lawrence and the adjoining
Atlantic coast, and to the dangers which thence arise to the navigation ;
(2) To urge upon the Government the importance of obtaining accurate
and systematic tidal observations, and of tabulating and reducing the
results by the scientific methods elaborated by Committees of the Associa
tion ; and (3) to suggest the immediate establishment of a sufficient
eeries of observing stations on the coast of the Dominion.'
A memorial in accordance with the above resolution was adopted
by the Council and forwarded to the Government of the Dominion of
Canada. To this a reply was received from the Canadian Minister of
Marine, expressing regret that the Dominion Government were unable
at the present time to undertake a special sui'vey of the tides and currents
in the Gulf of St. Lawrence. The Council, however, are not without
hope that the proposed observations may be regarded as deferred rather
than as refused.
' That the Council memorialise the Canadian Government as to the
urgent necessity of encouraging investigation and publication of reports
with respect to the physical characters, languages, social, industrial, and
artistic condition of the native tribes of the Dominion.'
A memorial in accordance with the above was also adopted by the
■Council and forwarded to the Government of the Dominion of Canada.
REPORT OF THE COUNCIL. Ixix
The receipt of this was acknowledged, and the Conncil were informed
that it would be duly considered by the Dominion Government.
' That the attention of the Council be drawn to the advisability of
communicating with the Admiralty for the purpose of urging on them
the importance of the employment of the Harmonic Analysis in the
Reduction of Admiralty Tidal Observations.'
The above recommendation was duly considered, but the Council,
while fully conscious of the importance of the subject, deemed the time
inopportune for pressing the matter on the attention of the Admiralty.
' That the Council be requested to examine the feasibility of insti
tuting a scheme for pi'omoting an International Scientific Congress, to meet
at intervals in different countries, and to report thereon to the General
Committee at the next meeting of the Association.'
This most important question has been very fully considered by the
Council during the past year. The importance of such a Congress can
hardly be doubted ; at the same time there are many serious difficulties in
devising a practical scheme, and many considerations to be taken into
account, before it would be prudent to undertake so great a departure
from the ordinary procedure of the Association, as would be involved by
such schemes as have seemed most feasible. The following is a brief
history of what has been done : At the conclusion of the Montreal Meeting
a Committee of the Council (of which Mr. Vernon Harcourt, the General
Secretary, was a member) took the opportunity of being present at the
meeting of the American Association at Philadelphia to confer with some
members of the Committee in America, from whom the latest and most
definite proposal of an International Scientific Association has emanated.
After returning to England, a letter was received by Mr. Vernon Harcourt
from Dr. S. C. Minot, Secretary to the above Committee, which was laid
before a Committee of the Council. As a result of their consideration of
this letter, the Secretary entered into an informal correspondence with
Dr. C. S. Minot. The intent of this correspondence was to bring about
an exchange of views and a discussion of certain difficulties which pre
sented themselves at first sight, and as it, in effect, contains the outline of
a scheme, the Council (with Dr. Minot's permission) have resolved to place
it, together with extracts from his letter to Mr. Vernon Harcourt, in the
hands of the General Committee. Copies of it are accordingly distributed
with this Report. The Council, in the next place, deemed it desirable to
ascertain what support the proposal of a joint meeting of the British
Association and of the International Scientific Association, in the suggested
rudimentary form, would meet with from the more important scientific
societies in London ; for, without their favourable countenance and the
permission to use the rooms of such as were couveniently situated, the
project would necessarily be abortive. A circular was accordingly ad
dressed to a number of the London scientific societies, with the result
that out of 29 societies which sent answers, three expressed their inability,
in consequence of formal difficulties, to reply at present ; two were
opposed to the scheme ; five were favourable ; and the rest were not
hostile. It should, however, be remarked, that while a willingness to
lend rooms was very generally shown, any approbation of the scheme was
expressed in very guarded terms, and amounted, in the majority of cases,
to little more than a nonexpression of disapproval. In these circum
stances the Council invite the General Committee to take the matter into
Ixx
REPORT — 1885.
tlieir consideration duriDg the Aberdeen Meeting, and suggest that the
second meeting of the General Committee would be the most convenient
opportunity for a discussion.
One vacancy in the Council has been caused by the lamented death
of Dr. Gwyn Jeffreys ; another by the resignation of Prof. Prestwich ; it
follows, therefore, that in accordance with the rule, three other members
will retire. The retiring members will be : —
Sir F. J. Evans. Prof. W. G. Adams.
The Right Hon. G. SclaterBooth.
The Council recommend the reelection of the other ordinary Members
of Council, with the addition of the gentlemen whose names are distin
guished by an asterisk in the following list : —
Abney, Capt. W. de W., F.R.S.
Ball, Prof. R. S., F.R.S.
Bateman, J. F. La Trobe, Esq.,
F.R.S.
*Blanford, W. T., Esq., F.R.S.
Bramwell, Sir F. J., F.R.S.
*Crookes, W., Esq., F.R.S.
Dawkins, Prof. W. Boyd, F.R.S.
De La Rue, Dr. Warren, F.R.S.
Dewar, Prof. J., F.R.S.
Flower, Prof. W. H., F.R.S.
Gladstone, Dr. J. H., F.R.S.
Glaisher, J. W. L., Esq., F.R.S.
GodwinAusten, Lieut.Col. H. H.,
F.R.S.
Hawkshaw, J. Clarke, Esq., F.G.S.
Henrici, Prof. O., F.R.S.
Hughes, Prof. T. McK., F.G.S.
*Martin, J. B., Esq., F.S.S.
*M'Leod, Prof. H., F.R.S.
Moseley, Prof. H. N., F.R.S.
Ommanney, Admiral Sir E., C.B.,
F.R.S.
Pengelly, W., Esq., F.R.S.
Perkin, Dr. W. H., F.R.S.
Sorby, Dr. H. C, F.R.S.
Temple, Sii R., Bart., G.C.S.I.
•ThiseltonDyer, W. T., Esq.,.
C.M.G., F.R.S.
Ixxi
Recommendations adopted by the General Committee at the
Aberdeen Meeting in September 1885.
[When Committees axe appointed, the Member first named is regarded as the
Secretary, except there is a specific nomination.]
Involving Grants of Money.
That Professor G. Carey Foster, Sir William Thomson, Professor
Ayrton, Professor J. Perry, Professor W. G. Adams, Lord Rayleigh,
Dr. 0. J. Lodge, Dr. Johu Hopkinson, Dr. A. Muirhead, Mr. W. H.
Preece, Mr. Herbert Taylor, Professor Everett, Professor Schuster, Dr.
J. A. Fleming, Professor G. F. Fitzgerald, Mr. R. T. Glazebrook, Professor
Chrystal, Mr. H. Tomlinson, Professor W. Garnett, Professor J. J.
Thomson, and Mr. TV". N. Shaw be reappointed a Committee for the
purpose of constructing and issuing practical Standards for use in
Electrical Measurements ; that Mr. Glazebrook be the Secretary, and
that the sum of 40/. be placed at their disposal for the purpose.
That Professor Balfour Stewart, Professor Schuster, Professor Stokes,
Mr. G. Johnstone Stoney, Professor Sir H. E. Roscoe, Captain Abney, and
Mr. G. J. Symons be reappointed a Committee for the purpose of con
sidering the best methods of recording the direct intensity of Solar Eadia
tion ; that Professor Balfour Stewart be the Secretary, and that the un
expended sum of 20Z. be placed at their disposal for the purpose.
That Professor Balfour Stewart (Secretary), Mr. Knox Laughton, Mr.
G. J. Symons, and Mr. R. H. Scott be reappointed a Committee, with
power to add to their number, for the purpose of cooperating with Mr.
E. J. Lowe in his project of establishing a Meteorological Observatory
near Chepstow on a permanent and scientific basis, and that the unex
pended sum of 25Z. be again placed at their disposal for the purpose.
That Professor G. H. Darwin, Sir W. Thomson, and Major Baird be
a Committee for the purpose of preparing instructions for the practical
work of Tidal Observation ; that Professor Darwin be the Secretary,
and that the sum of oOl. be placed at their disposal for the purpose.
That Professors Balfour Stewart and Sir W. Thomson, Sir J. H.
Lefroy, Sir Frederick Evans, Professor G. H. Darwin, Professor G.
Chrystal, Professor S. J. Perry, Mr. C. H. Carpmael, Professor Schuster,
Mr. G. M. Whipple, and Captain Creake be reappointed a Committee for
the purpose of considering the best means of comparing and reducing
Magnetic Observations ; that Professor Balfour Stewart be the Secretary,
and that the sum of 40Z. be placed at their disposal for the purpose.
That Professor G. Forbes, Captain Abney, Dr. J. Hopkinson,
Professor W. G. Adams, Professor G. C. Foster, Lord Rayleigh, Mr.
Preece, Professor Schuster, Professor Dewar, Mr. A. Vernon Har
court. Professor Ayrton, and Sir James Douglass be reappointed a Com
mittee for the purpose of reporting on Standards of Light ; that Professor
G. Forbes be the Secretary, and that the sum of 201. be placed at their
disposal for the purpose.
Ixxii EEPORT — 1885.
That Professor Crura Brown, Mr. MilneHome, Mr. John Murray,
and Mr. Bnchan be reappointed a Committee for the purpose of co
operating with the Scottish Meteorological Society in making meteoro
logical observations on Ben Nevis ; that Professor Crum Brown be the
Secretary, and that the sum of lOOZ. be placed at their disposal for the
purpose.
That Professors Armstrong, Lodge, and Sir William Thomson, Lord
Rayleigh, Professors Schuster, Poynting, J. J. Thomson, Fitzgerald, Crum.
Brown, Ramsay, Frankland, Tilden, and Hartlev, Captain Abney, Messrs.
W. N. Shaw, H. B. Dixon, J. T. Bottomley, W. Crookes, and Shelford
Bidwell, and Dr. Fleming be a Committee for the purpose of considering
the subject of Electrolysis in its Physical and Chemical bearings ; that
Professor Armstrong be the Chemical Secretary and Professor Lodge the
Physical Secretary, and that the sum of 20Z. be placed at their disposal
for the purpose.
That Professors McLeod and Ramsay and Mr. W. A. Shenstone be a
Committee for the further investigation of the Influence of the Silent
Discharge of Electricity on Oxygen and other gases ; that Mr. W. A.
Shenstone be the Secretary, and that the sum of 20Z. be placed at their
disposal for the purpose.
That Professors Williamson, Dewar, Frankland, Crum Brown, Odling,
and Armstrong, Drs. Hugo Miiller, A. G. Vernon Harcourt, F. R. Japp,
and H. Forster Morley, and ]\Iessrs. C. E. Groves, J. Millar Thomson, V. H.
Veley, and H. B. Dixon be reappointed a Committee for the purpose of
drawing up a statement of the varieties of Chemical Names which have
come into use, for indicating the causes which have led to their adoption,
and for considering what can be done to bring about some convergence
of the views on Chemical Nomenclature obtaining among English and
foreign chemists ; that Mr. H. B. Dixon be the Secretary, and that the
sum of bl. be placed at their disposal for the purpose.
That Mr. W. T. Blanford, Professor J. W. Judd, and Messrs. W. Car
ruthers, H. Woodward, and J. S. Gardner be reappointed a Committee
for the purpose of reporting on the Fossil Plants of the Tertiary and
Secondary Beds of the United Kingdom ; that Mr. J. S. Gardner be the
Secretary, and that the sum of 20L be placed at their disposal for the
purpose.
That Professor T. McK. Hughes, Dr. H. Hicks, Dr. H. Woodward,
and Messrs. E. B. Luxmoore, P. Pennant, and Edwin Morgan be a Com
mittee for the purpose of exploring the Caves of North Wales ; that
Dr. H. Hicks be the Secretary, and that the sum of 251. be placed at
their disposal for the purpose.
That Mr. R. Etheridge, Mr. T. Gray, and Professor John Milne be
reappointed a Committee for the purpose of investigating the Volcanic
Phenomena of Japan ; that Professor John Milne be the Secretary, and
that the sum of 501. be placed at their disposal for the purpose.
That Messrs. R. B. Grantham, C. E. De Ranee, J. B. Redman, W.
Topley, W. Whitaker, and J. W. Woodall, MajorGeneral Sir A. Clarke,
Admiral Sir E. Ommanney, Sir J. N. Douglass, Captain Sir F. J. O.
Evans, Captain J. Parsons, Captain W. J. L. Wharton, Professor J.
Prestwich, and Messrs. E. Fasten, J. S. Valentine, and L. F. Vernou
Harcourt be reappointed a Committee for the purpose of inquiring into
the Rate of Erosion of the Seacoasts of England and Wales, and the
Influence of the Artificial Abstraction of Shingle or other Material in that
RECOMMENDATIONS ADOPTED BY THE GENERAL COMMITTEE. Ixxiii
Action ; that Messrs. De Ranee and Topley be tlie Secretaries, and that
the sum of 20?. be placed at their disposal for the purpose.
That Messrs. H. Bauerman, F. W. Rndler, J. J. H. Teall, and H. J.
JohnstonLavis be reappointed a Committee for the purpose of investi
gating the Volcanic Phenomena of Vesuvius and its neighbourhood ; that
Mr. H. J. JohnstonLavis be the Secretary, and that the sum of 30?. be
placed at their disposal for the purpose.
That Dr. J. Evans, Professor W. J. Sollas, Dr. G J. Hinde, and Messrs.
W. CaiTuthers, R. B. Newton, J. J. H. Teall, F. W. Rudler, W. Topley,
W. Whitaker, and E. Wethered be a Committee for the purpose of carry
ing on the Geological Record ; that Mr. W. Topley be the Secretary, and
that the sum of 100?. be placed at their disposal for the purpose.
That Mr. R. Etheridge, Dr. H. Woodward, and Professor T. R. Jones
be reappointed a Committee for the purpose of reporting on the Fossil
Phyllopoda of the Palseozoic Rocks ; that Professor T. R. Jones be the
Secretary, and that the sum of 15?. be placed at their disposal for the
purpose.
Tbat Mr. Stainton, Sir John Lubbock,' and Mr. McLachlan be a
Committee for the purpose of continuing a Record of Zoological Litera
ture ; that Mr. Stainton be the Secretary, and that the sum of 100?. be
placed at their disposal for the purpose.
That Mr. John Murray, Professor Cossar Ewart, Professor Alleyne
Nicholson, Professor Mcintosh, Professor Young, Professor Struthers,
and Professor McKendrick be reappointed a Committee for the purposes
of a Marine Biological Station at Granton, Scotland ; that Mr. John
Murray be the Secretary, and that the sum of 75?. be placed at their dis
posal for the purpose.
That Professor Ray Lankester, Mr. P. L. Sclater, Professor M. Foster,
Mr. A. Sedgwick, Professor A. M. Marshall, Professor A. C. Haddon,
Professor Moseley, and Mr. Percy Sladen be reappointed a Committee for
the purpose of arranging for the occasional occupation of a table at the
Zoological Station at Naples ; that Mr. Percy Sladen be the Secretary,
and that the sum of 50?. be placed at their disposal for the purpose.
That Professor Cleland, Professor McKendrick, Professor Ewart,
Professor Stirling, Professor Bower, Dr. Cleghorn, and Professor Mcintosh
be a Committee for the purpose of continuing the Researches on Food
Fishes and Invertebrates at the Marine Laboratory, St. Andrews ; that
Professor Mcintosh be the Secretary, and that the sum of 75?. be placed
at their disposal for the purpose.
That Mr. J. Cordeaux, Mr. J. A. HarvieBrown, Professor Newton,
Mr. W. Eagle Clarke, Mr. R. M. Barrington, and Mr. A. G. More be
appointed a Committee for the purpose of obtaining (with the consent
of the Master and Elder Brethren of the Trinity House and the Commis
sioners of Northern and Irish Lights) observations on Migration at
Lighthouses and Lightvessels, and of reporting on the same ; that Mr.
J. Cordeaux be the Secretary, and that the sum of 30?. be placed at their
disposal for the purpose.
That Professor Cleland, Professor McKendrick, and Dr. McGregor
Robertson be a Committee for the purpose of investigating the
Mechanism of the Secretion of Urine ; that Dr. McGregor Robertson
be the Secretary, and that the sum of 10?. be placed at their disposal
for the purpose.
That General J. T. Walker, Sir J. H. Lefroy, Lieut. Colonel Godwin
Ixxiv REPORT — 1885.
Austen, Mr. W. T. Blanford, Mr. Sclater, Mr. Carruthers, Mr. Thiselton
Dyer, Professor Strnthers, Mr. G. W. Bloxam, Mr. H. W. Bates, Lord
Alfred Churcliill, Mr. F. Galton, Mr. J. S. O'Halloran, Mr. Coutts
Trotter, and Professor Moseley be a Committee for the purpose of
furthering the Exploration of New Guinea, by making a grant to Mr.
Forbes for the purposes of his Expedition ; that Mr. H. W. Bates be the
Secretary, and that the sum of 150/. be placed at their disposal for the
purpose.
That General J. T. Walker, Sir J. H. Lefroy, Sir William Thomson,
Mr. Alexander Buchan, Mr. J. Y. Buchanan, Mr. John Murray, Dr. Rae,
Mr. H. W. Bates, and Captain W. J. Dawson be a Committee for the
purpose of organising a systematic investigation of the Depth of the per
manently Frozen Soil in the Polar Regions, its geographical limits, and
relation 'to the present Pole of greatest cold ; that Mr. H. W. Bates be the
Secretary, and that the sum of 51. be placed at their disposal for the
purpose.
That Professor Sidgwick, Professor Foxwell, the Rev. W. Cunning
ham, and Professor Munro be a Committee for the purpose of inquiring
into the Regulation of Wages under the Sliding Scales ; that Professor
Munro be the Secretary, and that the sum of 10/. be placed at their dis
posal for the purpose.
That Mr. W. H. Barlow, Professor J. Thomson, Captain D. Galton,
Mr. B. Baker, Professor W. C. TJnwin, Professor A. B. W. Kennedy, Mr.
C. Barlow, Mr. A. T. Atchison, and Professor H. S. Hele Shaw be a
Committee for the purpose of obtaining information with reference ta
the Endurance of Metals under repeated and varying stresses, and the
proper working stresses on Railway Bridges and other structures subject
to varying loads ; that Mi\ A. T. Atchison be the Secretary, and that
the sum of 10/. be placed at their disposal for the purpose.
That Dr. Garson, Mr. Pengelly, Mr. P. W. Rudler, and Mr. _G. W..
Bloxam be a Committee for the purpose of investigating the Prehistoric
Race in the Greek Islands ; that Mr. Bloxam be the Secretary, and.
that the sum of 20^. be placed at their disposal for the purpose.
That Dr. E. B. Tylor, Dr. G. M. Dawson, General Sir J. H. Lefroy, Dr.
Daniel Wilson, Mr. R. G. Haliburton, and Mr. George W. Bloxam be
reappointed a Committee for the purpose of investigating and publishing
reports on the physical characters, languages, and industrial and social
condition of the North Western Tribes of the Dominion of Canada ; that
Mr. Bloxam be the Secretary, and that the sum of 50/. be placed at their
disposal for the purpose.
That Mr. Francis Galton, Dr. Beddoe, Mr. Brabrook, Professor
Cunningham, Professor Flower, Mr. J. Park Harrison, Professor A.
Macalister, Dr. Muirhead, Mr. F. W. Rudler, Professor Thane, and Dr.
Garson be reappointed a Committee for the purpose of defining the
Racial Characteristics of the Inhabitants of the British Isles ; that
Dr. Garson be the Secretary, and that the sum of 10/. be placed at their
disposal for the purpose.
Not involving Grants of Money.
That Mr. James N. Shoolbred and Sir William Thomson be reap
pointed a Committee for the purpose of reducing and tabulating the Tidal
Observations in the English Channel made with the Dover tidegauge,
EECOMMENDATIOMS ADOPTED BT THE GENERAL COMMITTEE. IxxV
and of connecting them with observations made on the French coast ;
and that Mr. Shoolbred be the Secretary.
That Professor Barrett, Professor Fitzgerald, and Professor Balfour
Stewart be a Committee for the pnrpose of reporting on the Molecular
Phenomena attending the Magnetisation of Iron ; and that Professor
Barrett be the Secretary.
That Professor G. H. Darwin and Professor J. C. Adams be reap
pointed a Committee for the Harmonic Analysis of Tidal Observations ;
and that Professor Darwin be the Secretary.
That Mr. John Murray, Professor Schuster, Sir William Thomson,
Professor Sir H. B. Roscoe, Professor A. S. Herschel, Captain W. de W.
Abney, Professor Bonney, Mr. R. H. Scott, and Dr. J. H. Gladstone be
reappointed a Committee for the purpose of investigating the practica
bility of collecting and identifying Meteoric Dust, and of considering the
question of undertaking regular observations in various localities ; and
that Mr. Murray be the Secretary.
That Professors A. Johnson, Macgregor, J. B. Cherriman, and H. J.
Bovey and Mr. C. Carpmael be reappointed a Committee for the purpose
of promoting Tidal Observations in Canada ; and that Professor Johnson
be the Secretary.
That Professor Sylvester, Professor Cayley, and Professor Salmon be
reappointed a Committee for the purpose of calculating Tables of the
Fundamental Invariants of Algebraic Forms ; and that Professor Cayley
be the Secretary,
That Professors Everett and Sir William Thomson, Mr. G. J. Symons,
Sir A. C. Ramsay, Dr. A. Geikie, Mr. J. Glaisher, Mr. Pengelly,
Professor Edward Hull, Professor Prestwich, Dr. C. Le Neve Foster,
Professor A. S. Herschel, Professor G. A. Lebour, Mr. A. B. Wynne,
Mr. Galloway, Mr. Joseph Dickinson, Mr. G. F. Deacon, Mr. E. Wethered,
and Mr. A. Strahan be reappointed a Committee for the purpose of
investigating the Rate of Increase of Underground Temperature down
wards in various Localities of Dry Land and under Water ; and that Pro
fessor Everett be the Secretary.
That Professor Cayley, Sir William Thomson, Mr. James Glaisher,
and Mr, J. W. L. Glaisher (Secretary) be reappointed a Committee for
the purpose of calculating certain tables in the Theory of Numbers
connected with the divisors of a number.
That Professors Tilden and Ramsay and Dr. W. W. J. Nicol be a
Committee for the purpose of investigating the subject of Vapour Pressures
and Refractive Indices of Salt Solutions ; and that Dr. W. W. J. Nicol
be the Secretary.
That Professors Ramsay, Tilden, Marshall, and W. L. Goodwin be
a. Committee for the purpose of investigating certain Physical Constants
of Solution, especially the expansion of saline solutions : and that Pro
fessor W. L. Goodwin be the Secretary.
That Professors W. A. Tilden and H. E. Armstrong be a Committee
for the purpose of investigating Isomeric Naphthalene Derivatives ; and
that Professor H, E. Armstrong be the Secretary.
That Professor Sir H. E. Roscoe, Mr. Lockyer, Professors Dewar,
Liveing, Schuster, W. N. Hartley, and Wolcott Gibbs, Captain Abney,
and Dr. Marshall Watts be a Committee for the purpose of preparing
a new series of Wavelength Tables of the Spectra of the Elements ^
and that Dr. Marshall Watts be the Secretary.
Ixxvi REPORT — 1885.
That Professors Dewar and A. W. Williamson, Dr. Marshall Watts,
Captain Abney, Dr. Johnstone Stoney, Professors W. N. Hartley, McLeod,
Carey Foster, A. K. Huntington, Emerson Reynolds, Reinold, and
Liveing, Lord Rayleigh, Professor Schuster, and Professor W. Chandler
Roberts be a Committee for the purpose of reporting upon the present
state of our knowledge of Spectrum Analysis ; and that Professor W.
Chandler Roberts be the Secretary.
That Professor E. Hull, Dr. H. W. Crosskey, Captain Douglas Galton,
Professor J. Prestwich, and Messrs. James Glaisher, E. B. Marten, G. H.
Morton, James Parker, W. Pengelly, James Plant, I. Roberts, Fox
Strangways, T. S. Stooke, G. J. Symons, W. Topley, Tylden Wright, E.
Wethered, W. Whitaker, and C. E. De Ranee be reappointed a Com
mittee for the purpose of investigating the Circulation of the Under
ground Waters in the Permeable Formations of England, and the Quality
and Quantity of the Waters supplied to various towns and districts from
these formations ; and that Mr. De Ranee be the Secretary.
That Professors J. Prestwich, W. Boyd Dawkins, T. McK. Hughes,
and T. G. Bonney, Dr. H. W. Crosskey, and Messrs. C. E. De Ranee,
H. G. Fordham, J. E. Lee, D. Mackintosh, W. Pengelly, J. Plant, and
R. H. Tiddeman be reappointed a Committee for the purpose of record
ing the position, height above the sea, lithological characters, size, and
origin of the Erratic Blocks of England, Wales, and Leland, reporting
other matters of interest connected with the same, and taking measures
for their preservation ; and that Dr. Crosskey be the Secretary.
That Sir A. Taylor, Professor Bayley Balfour, Dr. Crombie Brown,
Dr. Cleghorn, and Sir John Lubbock be a Committee for the purpose of
considering whether the condition of our Forests and Woodlands might
not be improved by the establishment of a Forest School.
That Sir Joseph D. Hooker, Sir George Nares, Mr. John Murray,
General J. T. Walker, Admiral Sir Leopold McClintock, Dr. W. B.
Carpenter, Mr. Clements Markbam, and Admiral Sir Erasmus Ommanney,
be a Committee for the purpose of drawing attention to the desirability
of further research in the Antarctic Regions, nearly half a century having
elapsed since the last exploration; and that Admiral Sir Erasmus
■Ommanney be the Secretary.
That General J. T. Walker, Sir J. H. Lefroy, Sir William Thomson,
Mr. Alexander Buchan, Mr. J. Y. Buchanan, Mr. John Murray, Mr.
Francis Galton, Mr. H. W. Bates, and Mr. E. G. Ravenstein, with
power to add to their number, be a Committee for the purpose of taking
into consideration the combination of the Ordnance and Admiralty Sur
veys, and the production of a bathohypsographical map of the British
Islands ; and that Mr. E. G. Ravenstein be the Secretary.
That General J. T. Walker, Sir William Thomson, Sir J. H. Lefroy,
General R. Strachey, Professor A. S. Herschel, Professor G. Chrystal,
Professor C. Niven, Professor J. H. Poynting, and Professor A. Schuster
be a Committee for the purpose of inviting designs for a good Differential
Gravity Meter in supersession of the pendulum, whereby satisfactory
results may be obtained, at each station of observation, in a few hours,
instead of the many days over which it is necessary to extend pendulum
observations ; and that Professor J. H. Poynting be the Secretary.
That Dr. J. H. Gladstone, Professor Armstrong, Mr. William Shaen,
Mr. Stephen Bourne, Miss Lydia Becker, Sir John Lubbock, Dr.
H. W. Crosskey, Sir Richard Temple, Sir Henry E. Roscoe, Mr. James
EECOMMENDATIONS ADOPTED BY THE GENERAL COMMITTEE. Ixxvil
Hey wood, and Professor N. Story Maskelyne be reappointed a Committee
for the purpose of continuing the inquiries relating to the teaching of
Science in Elementary Schools ; and that Dr. J. H. Gladstone be the
Secretary.
That the Corresponding Societies Committee, consisting of Mr. F.
Galton, Professor "Williamson, Captain Douglas Galton, Professor Boyd
Dawkins, Sir Rawson Rawson, Dr. Garson, Mr. J. Evans, Mr. J.
Hopkinson, Mr. Whitaker, Mr. Symons, Professor Meldola (Secretary),
and General Pitt Rivers, be reappointed.
That Mr. Mollison be requested to report on the present state of our
knowledge of the Mathematical Theory of Thermal Conduction.
That Mr. P. T. Main be requested to draw up a Report on our experi
mental knowledge of the Properties of Matter with respect to volume,,
pressure, temperature, and specific heat.
That Mr. Glazebrook be requested to continue his Report on Optics.
That Professor J. J. Thomson be requested to continue his Report on.
Electrical Theories.
Communications ordered to be printed in extenso in the Annual
Seport of the Association.
Mr. Meldrum's paper, ' A Tabular Statement of the dates at which,,
and the localities where Pumice or Volcanic Dust was seen in the
Indian Ocean ' (with one plate).
Professor 0. J. Lodge's paper ' On Electrolysis,' opening the discussion
on Electrolysis. ,
Mr. Barker's paper ' On Slaty Cleavage.'
That Mr. Whitaker be requested to enlarge his List of Works on the
Geology of Staffordshire by the addition of lists on Warwickshire and
Worcestershire, and that the same be printed in full in the Report.
Mr. Stephen Bourne's paper ' On the use of Index Numbers in the
Investigation of Trade Statistics.'
Mr. W. H. Preece's paper ' On the Strength of Telegraph Poles.'
Mr. A. S. Biggart's paper ' On the Forth Bridge Works,' with the
necessary plates.
Mr. J. N. Shoolbred's paper ' On the Electric Lighting of the Forth
Bridge.'
Mr. C. Barlow's paper ' On the Tay Bridge,' with the necessary plates^
Resolutions referred to the Council for Consideration, and Action if
desirable.
That the Council be requested to reconsider the proposal of holding a
General International Congress, and to report to the General Committee
thereon at the next Meeting of the Association.
That the Council be requested to consider the desirability of admitting
ladies as Officers of the Association, or as Members of the General or
Sectional Committees.
That the Council be requested to consider the advisability of renderino
the special Reports of the Association more accessible to the scientific
public by placing them on sale in separate form.
That the printed Reports on Special Subjects be oflPered for sale to
Ixxviii EEPOUT — 1885.
the general public at the time of the Meeting, or as soon afterwards as
possible.
That the Conncil be requested to so modify the Rules of the Associa
tion as to permit of a Sectional Meeting being held at an earlier hour
than eleven, and the Sectional Committee previously, due notice being
given to the Section on the previous day.
That a memorial be presented to H.M. Government requesting them
to enlarge the existing Agricultural Department of the Privy Conncil,
with the view of concentrating all administrative functions relating to
Agriculture in one fully equipped Board and Department of Agriculture.
That the Council be requested to consider and take steps, if they think
it desirable, to memorialise the Government to undertake the more
systematic collection and annual publication of Statistics of Wages, and a
periodical industrial census.
That a memorial be presented to H.M. Government in favour of the
establishment of a National School of Forestry.
i
SYNOPSIS jOF GEANTS OF MONEY. Ixxix
Synopsis of Grants of Money appropriated to Scientific Pur
poses by the General Committee at the Aberdeen Meeting in
September 1885. The Names of the Members entitled to
call on the General Treasurer for the respective Grants are
prefixed.
Mathematics and Physics.
£ s. d.
*Foster, Professoi G. Carey. — Electrical Standards 40
*Stewart, Professor Balfour. — Solar Radiation 20
*Stewart, Professor Balfour. — Meteorological Observations
at Chepstow 25
Darwin, Professor G. H. — Instructions for Tidal Observations 50
*Stewart, Professor Balfour. — Comparing and reducing Mag
netic Observations 40
*Forbes, Professor G. — Standards of Light , 20
*Brown, Professor Crum. — Ben Nevis Observatory 100
*Armstrong, Professor. — Physical and Chemical bearings of
Electrolysis 20
diemistry.
M'Leod, Professor. — Silent discharge of Electricity into at
mosphere 20
*Williamson, Professor A. W. — Chemical Nomenclature 6
Geology.
*Blanford, Mr. W. T.— Fossil plants of the Tertiary and
Secondary Beds 20
Hughes, Professor T. McK. — Caves of North Wales 25
*Etheridge, Mr. R. — Volcanic Phenomena in Japan 50
*Grantbam, R. B. — Erosion of Sea Coasts 20
♦Bauerman, Mr. H. — Volcanic Phenomena of Vesuvius 30
*E vans, Dr. J. — Geological Record 100
^Etheridge, Mr. R. — Fossil Phyllopoda 15
Carried forward ^600
* Eeappointed.
IXXX KEPOET 1885,
& s. d.
Brought forward 600
Biology.
*Stanton, Mr. H. T.— Zoological Record 100
*Mrirray, Mr. J. — Marine Biological Station at Grantham ... 75
*Lankester, Professor Ray. — Zoological Station at Naples ... 50
Cleland, Professor. — Researches in Food Fishes and Inver
tebrata at St. Andrews 75
*Cordeaux, Mr. J.— Migration of Birds 30
Cleland, Professor. — Mechanism of Secretion of Urine 10
Geography.
Walker, General J. T. — New Guinea Exploration 150 0'
Walker, General J. T. — Investigation into depth of perma
nently frozen soil in Polar Regions 5 0'
Economic Science and Statistics.
Sidgwick, Professor. — Regulation of Wages under sliding
scales 10
Mechanics.
Barlow, Mr. W. H. — Effect of varying stresses on metals ... 10
Anthropology. i
Garson, Dr. — Investigation into a prehistoric race in the
Greek Islands 20
*Tylor, Dr. E. B. — Investigation into North Western Tribes
ofCanada 50
*Galton, Mr. F. — Racial characteristics in British Isles 10
£1195
* Eeappointed.
The Annual Meeting in 1886.
The Meeting at Birmingham will commence on Wednesday, Sep
tember 1.
Place of Meeting in 1887 .
The Annual Meeting of the Association will be held at Manchester.
GENERAL SXATEMEST.
Ixxxi
General Statement of Sums ivhich have been paid on account of
Grants for Scientific Purposes.
1834.
Tide Discussions 20
1835.
Tide Discussions 62
British Fossil Ichthyology ■■■ 105
±'167
1836.
Tide Discussions 163
British Fossillchthyology ... 105
Thermometric Observations,
&c 50
Experiments on longcon
tinued Heat 17 1
EainGauges 9 13
Refraction Experiments 15
Lunar Nutation 60
Thermometers 15 6
£435
1837.
Tide Discussions 284 1
Chemical Constants 24 13 6
Lunar Nutation 70
Observations on Waves 100 12
Tides at Bristol 150
Meteorology and Subterra
nean Temperature 93 3
Vitrification Experiments ... 150
Heart Experiments 8 4 6
Barometric Observations 30
Barometers 11 18 6
£922 12 6
1838.
Tide Discussions 29
British Fossil Fishes 100
Meteorological Observations
and Anemometer (construc
tion) 100
Cast Lon (Strength of) 60
Animal and Vegetable Sub
stances (Preservation of) ... 19 1 10
Eailway Constants 41 12 10
Bristol Tides 50
Growth of Plants 75
Mud in Rivers 3 6 6
Education Committee 50
Heart Experiments 5 3
Land and Sea Level 267 8 7
Steamvessels 100
Meteorological Committee ... 31 9 5
£932 2 2
1839.
Fossillchthyology 110
Meteorological Observations
at Plymouth, &c 63 10
1885.
£ s. d.
Mechanism of Waves 144 2
Bristol Tides 35 18 6
Meteorology and Subterra
nean Temperature 21 11
Vitrification Experiments ... 9 4 7
CastIron Experiments 103
Railway Constants 28 7 2
Land and Sea Level 274 1 4
Steam vessels' Engines 100
Stars in Histoire Celeste 171 18 6
Stars in Lacaille 11
Stars in R.A.S. Catalogue ... 166 16 6
Animal Secretions 10 10
Steam Engines in Cornwall... 50
Atmospheric Air 16 1
Cast and Wrought Iron 40
Heat on Organic Bodies 3
Gases on Solar Spectrum 22
Hdurly Meteorological Ob
servations, Inverness and
Kingussie 49 7 8
Fossil Reptiles 118 2 9
Mining Statistics 50
£1595 11
1840.
Bristol Tides 100 a
Subterranean Temperature ... 13 13 6
Heart Experiments 18 19
Lungs Experiments 8 13
Tide Discussions 60
Land and Sea Level 6 11 1
Stars (Histoire Celeste) 242 10
Stars (Lacaille) 4 15
Stars (Catalogue) 264 0
Atmospheric Air 15 15
Water on Iron 10
Heat on Organic Bodies 7 &
Meteorological Observations . 52 17 6
Foreign Scientific Memoirs... 112 1 6
Working Population 100
School Statistics 50
Forms of Vessels 184 7
Chemical and Electrical Phe
nomena 40
Meteorological Observations
at Plymouth 80
Magnetical Observations 185 13 9
£1546 16 4
1841.
Observations on Waves 30
Meteorology and Subterra
nean Temperature 8
Actinometers 10
Earthquake Shocks 17
Acrid Poisons .. 6
Veins and Absorbents 3
Mud in Rivers 5
e
8
7
Ixxxii
KEPORT — 1885.
£ s. d.
Marine Zoology 15 12 8
Skeleton Maps 20
Mountain Barometers 6 18 6
Stars (Histoire Celeste) 185
Stars (Lacaille) 79 5
Stars (Nomenclature of) 17 19 6
Stars (Catalogue of ) 40
Water on Iron 50
Meteorological Observations
at Inverness 20
Meteorological Observations
(reduction of ) 25
Fossil Reptiles 50
Foreign Memoirs 62 6
Railvsray Sections 38 1
Forms of Vessels 193 12
Meteorological Observations
at Plymouth 55
Magnetical Observations 61 18 8
Fishes of the Old Red Sand
stone 100
Tides at Leith 50
Anemometer at Edinburgh ... 69 1 10
Tabulating Observations 9 6 3
Races of Men 5
Radiate Animals 2
£1235 10 U
1812.
Dynamometric Instruments . . 113 11 2
Anoplura Britannice 52 12
Tides at Bristol 59 8
GasesonLight 30 14 7
Chronometers 26 17 6
Marine Zoology 15
British Fossil Mammalia 100
Statistics of Education 20
Marine Steamvessels' En
gines 28
Stars (Tlistoire Celeste) ...... 69
Stars (Brit. Assoc. Cat. of) ... 110
Railway Sections 161 10
British Belemnites .. 50
Fossil Reptiles (publication
of Report) 210
Forms of Vessels 180
Galvanic Experiments on
Rocks 5 8 6
Meteorological Experiments
at Plymouth 68
Constant Indicator and Dyna
mometric Instruments 90
Force of Wind 10
Light on Growth of Seeds ... 8
Vital Statistics 50
Vegetative Power of Seeds ... 8 1 11
Questions on Human Race ... 7 9
£1449 17 8
1843.
Revision of the Nomenclature
of Stars 2
£ s. d.
Reduction of Stars, British
Association Catalogue 25
Anomalous Tides, Frith of
Forth 120
Hourly Meteorological Obser
vations at Kingussie and
Inverness 77 12 8
Meteorological Observations
at Plymouth 55
Whewell's Meteorological
Anemometer at Plymouth . 10
Meteorological Observations,
Osier's Anemometer at Ply
mouth 20
Reduction of Meteorological
Observations 30
Meteorological Instruments
and Gratuities 39 6
Construction of Anemometer
at Inverness 56 12 2
Magnetic Cooperation 10 8 10
Meteorological Recorder for
Kew Observatory 50
Action of Gases on Light 18 16 1
Establishment at Kew Ob
servatory, Wages, Repairs
Furniture, and Sundries ... 133 4 7
Experiments by Captive Bal
loons 81 8
Oxidation of the Rails of
Railways 20
Publication of Report on
Fossil Reptiles 40
Coloured Drawings of Rail
way Sections 147 18 3
Registration of Earthquake
Shocks 30
Report on Zoological Nomen
clature 10
Uncovering Lower Red Sand
stone near Manchester 4 4
Vegetative Power of Seeds ... 5 3
Marine Testacea (Habits of) . 10
Marine Zoology 10
Marine Zoology 2 14
Preparation of Report on Bri
tish Fossil Mammalia 100
Physiological Operations of
Medicinal Agents 20
Vital Statistics 36 5 8
Additional Experiments on
the Forms of Vessels 70
Additional Experiments on
the forms of Vessels 100
Reduction of Experiments on
the Forms of Vessels 100
Morin's Instrument and Con
stant Indicator 69 14 10
Experiments on the Strength
of Materials
6
8
11
... 60
£1565
10
2
GENERAL STATEMENT.
Ixsxiii
£ s. d.
184i.
Meteorological Observations
at Kingussie and Inverness 12
Completing Observations at
PljTuouth 35
Magnetic and Meteorological
Cooperation 25 8 4
Publication of the British
Association Catalogue of
Stars 35
Observations on Tides on the
East Coast of Scotland ... 100
Revision of the Nomenclature
of Stars 18i2 2 9 6
Maintaining the Establish
ment in Kew Observa
tory 117 17 3
Instruments for Kew Obser
vatory ... 56 7 3
Influence of Light on Plants 10
Subterraneous Temperature
in Ireland 5
Coloured Drawings of Rail
way Sections 15 17 6
Investigation of Fossil Fishes
of the Lower Tertiary Strata 100
Registering the Shocks of
Earthquakes 1842 23 11 10
Structure of Fossil Shells ... 20
Radiata and Mollusca of the
^gean and Red Seas 1842 100
Geographical Distributions of
Marine Zoology 1842 10
Marine Zoology of Devon and
Cornwall 10
Marine Zoology of Corfu 10
Experiments on the Vitality
of Seeds 9
Experiments on the Vitality
of Seeds 1842 8 7 3
Exotic Anoplura 15
Strength of Materials 100
Completing Experiments on
the Forms of Ships 100
Inquiries into Asphyxia 10
Investigations on the Internal
Constitution of Metals 50
Constant Indicator and Mo
rin's Instrument 1842 10
■ £981 12 "8
1845.
Publication of the British As
sociation Catalogue of Stars 351 14 6
Meteorological Observations
at Inverness 30 IS 11
Jlagnetic and Meteorological
Cooperation 16 16 8
Meteorological Instruments
at Edinburgh 18 11 9
Reduction of Anemometrical
Observations at Plymouth 25
£ s. d.
Electrical Experiments at
Kew Observatory 43 17 8
Maintaining the Establish
ment in Kew Observatory 149
For Kreil's Barometrograph 25
Gases from Iron Furnaces... 50
The Actinograph 15
Microscopic Structure of
Shells 20
Exotic Anoplura 1843 10
Vitality of Seeds 1843 2
Vitality of Seeds 1844 7
Marine Zoology of Cornwall 10
Physiological Action of Medi
cines 20
Statistics of Sickness and
Mortality in York 20
Earthquake Shocks 18 43 15 14 8
£831 9~~9
15
7
1847.
Computation of the Gaussian
Constants for 1829 50
Habits of Marine Animals ... 10
Physiological Action of Medi
cines 20
Blarine Zoology of Cornwall 10
Atmospheric Waves 6
Vitality of Seeds 4
Maintaining the Establish
ment at Kew Observatory 107
£208
1846.
British Association Catalogue
of Stars 1844 211 15
Fossil Fishes of the London
Clay 100
Computation of the Gaussian
Constants for 1829 50
Maintaining the Establish
ment at Kew Observatory 146
Strength of Materials 60
Researches in Asphyxia 6
Examination of Fossil Shells 10
Vitality of Seeds 1 844 2
Vitality of Seeds 1845 7
Marine Zoology of Cornwall 10
Marine Zoology of Britain ... 10
Exotic Anoplura 1814 25
Expenses attending Anemo
meters 11
Anemometers' Repairs 2
Atmospheric Waves 3
Captive Balloons 1844 8
Varieties of the Human Race
1844 7 6 3
Statistics of Sickness and
Mortality in York 12
£685 16
16
7
16
2
15
10
12
3
7
6
3
6
3
3
19
8
9
3
7
7
8 6
5 4
62
Ixxxiv
KEPORT — 1885.
£ s. d.
1848.
Maintainingr the Establish
ment at Kew Observatory 171 15 11
Atmospheric Waves 3 10 9
Vitality of Seeds 9 15
Completion of Catalogue of
Stars 70
On Colouring Matters 5
On Growth of Plants •• 15
£275 1 8
1819.
Electrical Observations at
Kew Observatory 50
Maintaining the Establish
ment at ditto 76 2 5
Vitality of Seeds 5 8 1
On Growth of Plants 5
Kegistration of Periodical
Phenomena 10
Bill on Account of Anemo
metrical Observations 1 3 9
£169 19 6
1850.
Maintaining the Establish
ment at Kew Observatory 255 18
Transit of Earthquake "Waves 50
Periodical Phenomena 15
Meteorological Instruments,
Azores 25
£345 18
1851
Maintaining the Establish
ment at Kew Observatory
(includes part of grant in
1849) 309 2 2
Theory of Heat 20 1 1
Periodical Phenomena of Ani
mals and Plants 5
Vitality of Seeds 5 6 4
Influence of Solar Kadiation 30
Ethnological Inquiries 12
Researches on Annelida 10
£391 9~7
1852.
Maintaining the Establish
ment at Kew Observatory
(including balance of grant
for 1850)... 233 17 8
Experiments on the Conduc
tion of Heat 5 2 9
Influence of Solar Radiations 20
Geological Map of Ireland ... 15
Researches on the British An
nelida 10
Vitality of Seeds 10 6 2
Strength of Boiler Plates 10
£304 6 7
£ ». d.
1853.
Maintaining the Establish
ment at Kew Observatory 165
Experiments on the Influence
of Solar Radiation 15
Researches on the British
Annelida 10
Dredging on the East Coast
of Scotland 10
Ethnological Queries ^^ 5_
£205 a
1854.
Maintaining the Establish
ment at Kew Observatory
(including balance of
former grant) 330 15 4
Investigations on Flax 11
Effects of Temperature on
Wrought Iron 10
Registration of Periodical
Phenomena 10
British Annelida 10
Vitality of Seeds 5 2 3
Conduction of Heat 4 2
£380 19 7
18.55.
Maintaining the Establish
ment at Kew Observatory 425
Earthquake Movements 10
Physical Aspect of the Moon 118 5
Vitality of Seeds 10 7 11
Map of the World 15
Ethnological Queries 5
Dredging near Belfast .^ 4
£480T6~^
575
1856.
Maintaining the Establish
ment at Kew Observa
tory:—
1854 £ 75 0\
1855 £500 0/
Strickland's Ornithological
Synonyms 100
Dredging and Dredging
Forms 9 13
Chemical Action of Light ... 20 Or
Strength of Iron Plates 10
Registration of Periodical
Phenomena 10
Propagation of Salmon 10
£734 13 9
1857.
Maintaining the Establish
ment at Kew Observatory 350
Earthquake Wave Experi
ments 40
Dredging near Belfast 10 O'
Dredging on the West Coast
of Scotland 10 a
GENERAL STATEMENT.
Ixxxv
5 7
4
... 5
£507 15
4
£ s. d.
Investigations into the Mol
lusca of California 10
Experiments on Flax 5
Natural History of Mada
gascar 20
Researches on British Anne
lida 25
Eeport on Natural Products
imported into Liverpool ... 10
Artificial Propagation of Sal
mon 10
Temperature of Mines 7 8
Thermometers for Subterra
nean Observations
Lifeboats
18.58.
Maintaining the Establish
ment at Kew Observatory 500
Earthquake Wave Experi
ments 25
Dredging on the West Coast
of Scotland 10
Dredging near Dublin 5
Vitality of Seeds 5 5
Dredging near Belfast 18 13 2
Report on the British Anne
lida 25
Experiments on the produc
tion of Heat by Motion in
Fluids 20
Report on the Natural Pro
ducts imported into Scot
land 10
£618 18 2
1859.
Maintaining the Establish
ment at Kew Observatory 500
Dredging near Dublin 15
Osteology of Birds 50
Irish Tunicata 5
Manure Experiments 20
British Medusidas 5
Dredging Committee 5
Steamvessels' Performance... 5
Marine Fauna of South and
AVest of Ireland 10
Photographic Chemistry 10
Lanarljshire Fossils 20 1
Balloon Ascents 39 11
£684 11 1
1860.
Maintaining the Establish
ment at Kew Observatory 500
Dredging near Belfast 16 6
Dredging in Dublin Bay 15
Inquiry into the Performance
of Steamvessels ]24
Explorations in the Yellow
Sandstone of Dura Don ... 20
Chemicomechanical Analysis
of Rocks and Minerals 25
Researches on the Growth of
Plants 10
Researches on the Solubility
of Salts 30
Researches on the Constituents
of Manures 25
Balance of Captive Balloon
Accounts 1
». d,
13 6
£766 19 6
1861.
Maintaining the Establish
ment of Kew Observatory.. 500
Earthquake Experiments 25
Dredging North and East
Coasts of Scotland 23
Dredging Committee : —
1860 £50 \
1861 £22 0/
Excavations at Dura Den 20
Solubility of Salts 20
Steam vessel Performance ... 150
Fossils of Lesmahago 15
Explorations at Uriconium... 20
Chemical Alloys 20
Classified Index to the Trans
actions 100
Dredging in the Mersey and
Dee 5
Dip Circle 30
Photoheliographic Observa
tions 50
Prison Diet 20
Gauging of Water 10
Alpine Ascents 6
Constituents of Manures 25
72
5
10
£1111 5 10
1862.
Maintaining the Establish
ment of Kew Observatory 500
Patent Laws 21
Mollusca of N. W. of America 10
Natural History by Mercantile
Marine 5
Tidal Observations 25
Photoheliometer at Kew 40
Photographic Pictures of the
Sun 150
Rocks of Donegal 25
Dredging Durham and North
umberland 25
Connexion of Storms 20
Dredging Northeast Coast
of Scotland 6
Ravages of Teredo 3
Standards of Electrical Re
sistance 50
Railway Accidents 10
Balloon Committee 200
Dredging Dublin Bay 10
6
9
6
11
Jxxxvi
repout — 1885.
£ s. d.
Dredging the Mersey 5
Prison Diet 20
Gauging of Water 12 10
Steamships' Performance 150
Thermo Electric Currents 5
£1293 16 6
18C3.
Maintaining the Establish
ment of Kew Observatory.. 600
Balloon Committee deficiency 70
Balloon Ascents (other ex
penses) 25
Entozoa 25
Coal Fossils 20
Herrings 20
Granites of Donegal 5
Prison Diet 20
Vertical Atmospheric Move
ments 13
Dredging Shetland 50
Dredging Northeast coast of
Scotland 25
Dredging Northumberland
and Durham 17
Dredging Committee superin
tendence 10
Steamship Performance 100
Balloon Committee 200
Carbon under pressure 10
Volcanic Temperature 100
Bromide of Ammonium 8
Electrical Standards 100
Electrical Construction and
Distribution 40
Luminous Meteors 17
Kew Additional Buildings for
Photoheliograph 100
ThermoEIectricity 15
Analysis of Eocks 8
Hydroida 10
£1608
3 10
3 10
1864.
Maintaining tlie Establish
ment of Kew Observatory.. 600
Coal Fossils 20
Vertical Atmospheric Move
ments 20
Dredging Shetland 75
Dredging Northumberland... 25
Balloon Committee 200
Carbon under pressure 10
Standards of Electric Ke
sistance 100
Analysis of Piocks 10
Hydroida 10
Askham's Gift 50
Nitrite of Amyle 10
Nomenclature Committee ... 5
EainGauges 19 15 8
Castiron Investigation 20
£ s. d
Tidal Observations in the
Humber 50
Spectral Kays 45
Luminous Meteors 20
£1289 15 8
1865. — — — —
Maintaining the Establish
ment of kew Observatory.. 600
Balloon Committee 100
Hydroida 13
EainGauges 30
Tidal Observations in the
Humber 6 8
Hexylic Compoimds 20
Amyl Compounds 20
Irish Flora 25
American Mollusca 3 9
Organic Acids 20
Lingula Flags Excavation ... 10
Eurj^Dterus 50
Electrical Standards 100
Malta Caves Eesearches 30
Oyster Breeding 25
Gibraltar Caves Eesearches... 150
Kent's Hole Excavations 100
Moon's Surface Observations 35
Marine Fauna 25
Dredging Aberdeenshire 25
Dredging Channel Islands ... 50
Zoological Nomenclature 5
Eesistance of Floating Bodies
inAVater 100
Bath Waters Analysis 8 10 10
Luminous Meteors 40
£1591 7 10
1866.
Maintaining the Establish
ment of Kew Observatory. . 600
Lunar Committee 64 13 4
Balloon Committee 50
Metrical Committee 60
British Eainfall 50
Kilkenny Coal Fields 16
Alum Bay Fossil LeafBed ... 15
Luminous Meteors 50
Lingula Flags Excavation ... 20
Chemical Constitution of
Cast Iron 60
Amyl Compotinds 25
Electrical Standards 100
Malta Caves Exijloration 30
Kent's Hole Exploration 200
Marine Fauna, &c., Devon
and Cornwall 25
Dredging Aberdeenshire Coast 25
Dredging Hebrides Coast ... 60
Dredging the Mersey 5
Eesistance of Floating Bodies
in Water 60
Polycyanidesof Organic Eadi
cals 29
GENERAL STATEMENT.
Ixxxvii
£ s. d.
Riffor Mortis 10
Irish Annelida 15
Catalogue of Crania 50
Didine Birds of Mascarene
Islands 50
Tj'pical Crania Researches ... 30
Palestine Exploration Fun d... 100
:gl750 13 4
1867.
Maintaining the Establish
ment of Kew Observatory.. 600
Meteorological Instruments,
Palestine..... 50
Lunar Committee 120
Metrical Committee 30
Kent's Hole Explorations ... 100
Palestine Explorations 50
Insect Fauna, Palestine 30
British Rainfall 50
Kilkenny Coal Fields 25
Alum Bay Fossil Leaf Bed ... 25
Luminous Meteors 50
Bournemouth, &c., LeafBeds 30
Dredging Shetland 75
Steamship Reports Condensa
tion 100
Electrical Standards 100
Ethyl and Methyl series 25
Fossil Crustacea 25
Sound under Water 24 4
North Greenland Fauna 75
Do. Plant Beds 100
Iron and Steel Manufacture... 25
Patent Laws 30
£1739 4
1868.
Maintaining the Establish
ment of Kew Observatory. . 600
Lunar Committee 120
Metrical Committee 50
Zoological Record 100
Kent's Hole Explorations ... 150
Steamship Performances 100
British Rainfall 50
Luminous Meteors 50
Organic Acids 60
Fossil Crustacea 25
Methyl Series 25
Mercury and Bile 25
Organic Remains in Lime
stone Rocks 25
Scottish Earthquakes 20
Fauna, Devon and Cornwall.. 30
British Fossil Corals 50
Bagshot LeafBeds 50
Greenland Explorations 100
Fossil Flora : 25
Tidal Observations 100
Underground Temperature ... 50
Spectroscopic Investigations
of Animal Substances 5
Secondary Reptiles, &c 30
British Marine Invertebrate
Fauna . 100
£1'J40
1869. *^^^
Maintaining the Establish
ment of Kew Observatory. . 600
Lunar Committee 50
Metrical Committee 25
Zoological Record 100
Committee on Gases in Deep
well Water 25
British Rainfall 50
Thermal Conductivity of Iron,
&c 30
Kent's Hole Explorations 150
Steamship Performances 30
Chemical Constitution of
Cast Iron 80
Iron and Steel Manufacture 100
Methyl Series 30
Organic Remains in Lime
stone Rocks 10
Earthquakes in Scotland 10
British Fossil Corals 50
Bagshot LeafBeds 30
Fossil Flora 25
Tidal Observations 100
Underground Temperature ... 30
Spectroscopic Investigations
of Animal Substances 5
Organic Acids 12
Kiltorcan Fossils 20
Chemical Constitution and
Physiological Action Rela
tions 15
Mountain Limestone Fossils 25
Utilization of Sewage 10
Products of Digestion 10
£1622'
1870.
Maintaining the Establish
ment of Kew Observatory 600
Metrical Committee 25
Zoological Record 100
Committee on Marine Fauna 20
Ears in Fishes 10
Chemical Nature of Cast Iron 80
Luminous Meteors 30
Heat in the Blood 15
British Rainfall 100
Thermal Conductivity of
Iron, &c : 20
British Fossil Corals 50
Kent's Hole Explorations ... 150
Scottish Earthquakes 4
Bagshot Leaf Beds 15
Fossil Flora 25
Tidal Observations 100
Underground Temperature ... 50
Kiltorcan Quarries Fossils ... 20
«. d.
Ixxxviii
EEPORT — 1885.
£
Mountain Limestone Fossils 25
Utilization of Sewage 50
Organic Chemical Compounds 30
Onny River Sediment 3
Mechanical Equivalent of
Heat ••• 50
£1572
J871.
Maintaining the Establish
ment of Kew Observatory 600
Monthly Reports of Progi'ess
in Chemistry 100
Metrical Committee 25
Zoological Record 100
Thermal Equivalents of the
Oxides of Chlorine 10
Tidal Observations 100
Fossil Flora 25
Luminoiis Meteors 30
British Fossil Corals 25
Heat in the Blood 7
British Rainfall 50
Kent's Hole Explorations ... 150
Fossil Crustacea 25
Methyl Compounds 25
Lunar Objects 20
Fossil Coral Sections, for
Photographing 20
Bagshot LeafBeds 20
Moab Explorations 100
Gaussian Constants 40
£1472
1872.
Maintaining the Establish
ment of Kew Observatory 300
Metrical Committee 75
Zoological Record 100
Tidal Committee 200
Carboniferous Corals 25
Organic Chemical Compounds 25
Exploration of Moab 100
TeratoEmbryological Inqui
ries 10
Kent's Cavern Exploration.. 100
Luminous Meteors 20
Heat in the Blood 15
Fossil Crustacea 25
Fossil Elephants of Malta ... 25
Lunar Objects 20
Inverse WaveLengths 20
British Rainfall 100
Poisonous Substances Antago
nism 10
Essential Oils, Chemical Con
stitution, &c 40
Mathematical Tables 50
Thermal Conductivity of Me
tals
s. d.
2
6
2 6
.... 25
£1285
£ s. d.
1873.
Zoological Record 100
Chemistry Record 200
Tidal Committee 400
Sewage Committee 100
Kent's Cavern Exploration ... 150
Carboniferous Corals 25
Fossil Elephants 25
WaveLengths 150
British Rainfall 100
Essential Oils 30
Mathematical Tables 100
Gaussian Constants •.... 10
SubWealden Explorations... 25
Underground Temperature ... 150
Settle Cave Exploration 50
Fossil Flora, Ireland 20
Timber Denudation and Rain
fall 20
Luminous Meteors .'^O
£1685
1874. "* ■
Zoological Record 100
Chemistry Record 100
Mathematical Tables 100
Elliptic Functions 100
Lightning Conductors 10
Thermal Conductivity of
Rocks 10
Anthropological Instructions,
&c 50
Kent's Cavern Exploration... 150
Luminous Meteors 30
Intestinal Secretions 15
British Rainfall 100
Essential Oils 10
SubWealden Explorations... 25
Settle Cave Exploration 50
Mauritius Meteorological Re
search 100
Magnetization of Iron 20
Marine Organisms 30
Fossils, North West of Scot
land 2 10
Physiological Action of Light 20
Trades Unions 25
Mountain LimestoneCorals 25
Erratic Blocks 10
Dredging, Durham and York
shire Coasts 28 5
High Temperature of Bodies 30
Siemens 's Pyrometer 3 6
Labyrinthodonts of Coal
Measures 7 15
£1151 16
1875.
Elliptic Functions 100
Magnetization of Iron 20
British Rainfall 120
Luminous Meteors 30
Chemistry Record 100
GENERAL STATEMENT.
Ixxxix
£ s. d.
Specific Volume of Liquids... 25
Estimation of Potash and
Phosphoric Acid 10
Isometric Cresols 20
Sub Wealden Explorations... 100
Kent's Cavern Exploration... 100
Settle Cave Exploration 50
Earthquakes in Scotland 15
Underground Waters 10
Development of Myxinoid
Fishes 20
Zoological Record 100
Instructions for Travellers ... 20
Intestinal Secretions 20
Palestine Exploration 100
£960
1876.
Printing Mathematical Tables 159 4 2
British Rainfall 100
Ohm's Law 9 15
Tide Calculating Machine ... 200
Specific Volume of Liquids... 25
Isomeric Cresols 10
Action of Ethyl Bromobuty
rate on Ethyl Sodaceto
acetate 5
Estimation of Potash and
Phosphoric Acid 13
Exploration of Victoria Cave,
Settle 100
Geological Record 100
Kent's Cavern Exploration... 100
Thermal Conductivities of
Rocks 10
Underground Waters 10
Earthquakes in Scotland 1 10
Zoological Record 100
Close Time 5
Physiological Action of Sound 25
Zoological Station 75
Intestinal Secretions 15
Physical Characters of Inha
bitants of British Isles 13 15
Measuring Speed of Ships ... 10
Effect of Propeller on turning
of Steam Vessels 5
£1092 4 2
1877.
Liquid Carbonic Acids in
Minerals 20
Elliptic Functions 250
Thermal Conductivity of
Rocks 9 11 7
Zoological Record 100
Kent's Cavern 100
Zoological Station at Naples 75
Luminous Aleteors 30
Elasticity of Wires 100
Dipterocarpse, Report on 20
£ «. d.
Mechanical Equivalent of
Heat 35
Double Compounds of Cobalt
and Nickel 8
Underground Temperatures 50
Settle Cave Exploration 100
Underground Waters in New
Red Sandstone 10
Action of Ethyl Bromobuty
rate on Ethyl Sodaceto
acetate 10
British Earthworks 25
Atmospheric Elasticity in
India 15
Development of Light from
Coalgas 20
Estimation of Potash and
Phosphoric Acid 1 18
Geological Record 100
Anthropometric Committee 34
Physiological Action of Phos
phoric Acid, &c 15
£1128 9 7
1878.
Exploration of Settle Caves 100
Geological Record 100
Investigation of Pulse Pheno
mena by means of Syphon
Recorder 10
Zoological Station at Naples 75
Investigation of Underground
Waters 15
Transmission of Electrical
Impulses through Nerve
Structure 30
Calculation of Factor Table
of Fourth Million 100
Anthropometric Committee... 66
Chemical Composition and
Structure of less known
Alkaloids 25
Exploration of Kent's Cavern 50
Zoological Record 100
Fermanagh Caves Exploration 15
Thermal Conductivity of
Rocks 4 16 6
Luminous Meteors 10
Ancient Earthworks 25
£725 16 6
1879.
Table at the Zoological
Station, Naples 75
Miocene Flora of the Basalt
of the North of Ireland ... 20
Illustrations for a Monograph
on the Mammoth 17
Record of Zoological Litera
ture 100
Composition and Structure of
lessknown Alkaloids ^  25
xc
REPORT — 1 885.
£ s. d.
Exploration of Caves in
Borneo 50
Kent's Cavern Exploration... 100
Kecord of the Progress of
Geology 100
Fermanagh Caves Exploration 5
Electrolysis of Metallic Solu
tions and Solutions of
Compound Salts 25
Anthropometric Committee... 50
Natural History of Socotra... 100
Calculation of Factor Tables
for 5th and 6th Millions ... 150
Circulation of Underground
Waters 10
Steering of Screw Steamers... 10
Improvements in Astrono
mical Clocks 30
Marine Zoology of South
Devon 20
Determination of Mechanical
Equivalent of Heat 12 15 6
Specific Inductive Capacity
of Sprengel Vacuum 40
Tables of Sunheat Co
efficients 30
Datum Level of the Ordnance
Survey 10
Tables of Fundamental In
variants of Algebraic Forms 36 14 9
AtmosiDheric Electricity Ob
servations in Madeira 15
Instrument for Detecting
Firedamp in Mines 22
Instruments for Measuring
the Speed of Ships 17 1 8
Tidal Observations in the
English Channel 10
£1 080 11 11
1880.
New Form of High Insulation
Key 10
Underground Temperature ... 10
Determination of the Me
chanical Equivalent of
Heat 8 6
Elasticity of Wires 50
Luminous Meteors 30
Lunar Disturbance of Gravity 30
Fundamental Invariants 8 5
Laws of Water Friction 20
Sj)ecific Inductive Capacity
of Sprengel Vacuum 20
Comp)letion of Tables of Sun
heat Coefficients 50
Instrument for Detection of
Firedamp in Mines 10
Inductive Capacity of Crystals
and Paraffines 4 17 7
Report on Carboniferous
Polyzoa 10
£ s. d.
Caves of South Ireland 10
Viviparous Nature of Ichthyo
saurus 10
Kent's Cavern Exploration... 60
Geological Record 100
l\Iiocene Flora of the Basalt
of North Ireland 15
Underground Waters of Per
mian Formations 5
Record of Zoological Litera
ture 100
Table at Zoological Station
at Naples 76
Investigation of the Geology
and Zoology of Mexico 50
Anthropometry 50
Patent Laws 5
£731 7 7
1881.
Lunar Disturbance of Gravity 30
Underground Temperature ... 20
High Insulation Key 5
Tidal Observations 10
Fossil Polyzoa 10
Underground Waters 10
Earthquakes in Japan 25
Tertiary Flora 20
Scottish Zoological Station ... 50
Naples Zoological Station ... 75
Natural History of Socotra ... 50
Zoological Record 100
Weights and Heights of
Human Beings 30
Electrical Standards 25
Anthropological Notes and
Queries 9
Specific Refractions 7
£476
1882.
Tertiarj' Flora of North of
Ireland 20
Exploration of Caves of South
of Ireland 10
Fossil Plants of Halifax 15
Fundamental Invariants of
Algebraical Forms 76
Record of Zoological Litera
ture 100
British Polyzoa 10
Naples Zoological Station ... 80
Natural History of Timor laut 100
Conversion of Sedimentary
Materials into Metamorphic
Rocks 10
Natural History of Socotra... 100
Circulation of Underground
Waters 15
Migration of Birds 15
Earthquake Phenomena of
Japan 25
3 1
3 1
1 11
GENERAL STATEMENT.
XCl
&
Geological Map of Europe ... 25
Elimination of Nitrogen by
Bodily Exercise 50
Anthropometric Committee... 50
Photograpliing Ultra Violet
Spark Spectra 25
Exploration of Kaygill Fis
sure 20
Calibration of Mercurial Ther
mometers 20
Wavelength Tables of Spec
tra of Elements 50
Geological Eecord 100
Standards for Electrical
Measurements 100
Exploration of Central Africa 100
Albuminoid Substances of
Serum 10
£1126
1883.
Natural History of Timorlaut 50
British Fossil iPolyzoa 10
Circulation of Underground
Waters 15
Zoological Literature Eecord 100
Exploration of Mount Kili
manjaro 500
Erosion of Seacoast of Eng
land and Wales 10
Fossil Plants of Halifax 20
Elimination of Nitrogen by
Bodily Exercise 38
Isomeric Naphthalene Deri
vatives 15
Zoological Station at Naples 80
Investigation of Loughton
Camp 10
Earthquake Phenomena of
Japan 50
Meteorological Observations
on Ben Nevis 50
Fossil Phyllopoda of Palaeo
zoic Eocks 25
Migration of Birds 20
Geological Eecord 50
Exploration of Caves in South
of Ireland 10
Scottish Zoological Station... 25
Screw Gauges 5
£1083~
1884.
Zoological Literature Eecord 100
Fossil Polyzoa 10
Exploration of Mount Kili
manjaro, East Africa 500
Anthropometric Committee... 10
Fossil Plants of Halifax 15
International Geological Map 20
Erratic Blocks of England ... 10
Natural History of Timorlaut 50
s. d.
1 11
3
3
3
3
£ s. d.
Coagulation of Blood 100
Naples Zoological Station ... 80
Bibliography of Groups of
Invertebrata 50
Earthquake Phenomena of
Japan 75
Fossil Phyllopoda of Paleo
zoic Eocks 15
Meteorological Observatory at
Chepstow 25
Migration of Birds 20
Collecting and Investigating
Meteoric Dust 20
Circulation of Underground
Waters 5
Ultra Violet Spark Spectra ... 8 4
Tidal Observations 10
Meteorological Observations
on Ben Nevis 50
£1173 4
1885.
Zoological Literature Eecord. 100
Vapour Pressures, &c., of Salt
Solutions 25
Physical Constants of Solu
tions 20
Eecent Polyzoa 10
Naples Zoological Station ... 100
Exploration of Mount Kilima
njaro 25
Fossil Plants of British Ter
tiary and Secondary Beds . 50
Calculating Tables in Theory
of Numbers 100
Exploration of New Guinea... 200
Exploration of Mount Eo
raima 100
Meteorological Observations
on Ben Nevis 50
Volcanic Phenomena of Vesu
vius 25
Biological Stations on Coasts
of United Kingdom 150
Meteoric Dust 70
Marine Biological Station at
Granton loo
Fossil Phyllopoda of Palajozoic
Eocks 25
Migration of Birds 30
Synoptic Chart of Indian
Ocean 50
Circulation of Underground
Waters 10
Geological Eecord 50
Eeduction of Tidal Observa
tions 10
Earthquake Phenomena of
Japan 70
Eaygill Fissure 15
£1385 6
XCii BEPOET — 1885.
General Meetings.
On Wednesday, September 9, at 8 p.m., in tlie Music Hall, the Right
Hon. Lord Rayleigh, M.A., D.C.L., LL.D., F.R.S., F.R.A.S., F.R.G.S.,
resigned the office of President to the Right Hon. Sir Lyon Playfair,
K.C.B., M.P., Ph.D., LL.D., F.R.S. L. & B., F.C.S., who took the Chair,
and delivered an Address, for which see page 1.
On Thursday, September 10, at 8 p.m., a Soiree took place in the Art
Gallery.
On Friday, September 11, at 8 p.m., in the Music Hall, Professor
W. G. Adams, M.A., F.R.S., F.G.S., delivered a Discourse on ' The
Electric Light and Atmospheric Absorption.'
On Monday, September 14, at 8.30 p.m., in the Music Hall, Mr. John
Murray, F.R.S.E., delivered a Discourse on ' The Great Ocean Basins.'
On Tuesday, September 15, at 8 p.m., a Soiree took place in the Art
Gallery.
On Wednesday, September 16, at 2.30 p.m., the concluding General
Meeting took place in St. Katherine's Hall, when the Proceedings of the
General Committee and the Grants of Money for Scientific purposes
were explained to the Members.
The Meeting was then adjourned to Birmingham. [The Meeting is
appointed to commence on Wednesday, September 1, 1886.]
PEE SIDE NT'S ADDEESS.
1885.
ADDEESS
BY
THE EIGHT HOX. SHI LYON PLAYFAIE,
K.C.B., M.P., F.R.S.
PRESIDENT.
I. Visit to Canada.
OuE meeting at Montreal was a notable event in the life of the Brit
ish Association, and even marked a distinct epoch in the histoiy of
civilisation. It was by no mere accident that the constitntion of the
Association enabled it to embrace all parts of the British Empire. Science
is truly catholic, and is bounded only by the universe. lu relation to
our vast empire, science, as well as literature and art, is the common
possession of all its varying people. The United Kingdom is limited to
120,800 square miles, inhabited by 35 millions of people ; but the empire
as a whole has 8^ millions of square miles, with a population of 305 millions.
To federate such vast possessions and so teeming a population into a political
unit is a work only to be accomplished by the labours and persistent
efforts of perhaps several generations of statesmen. The federation of its
science is a subject of less dimensions well within the range of experi
ment. No part of the British Empire was more suited than Canada to
try whether her science could be federated with our science. Canada
has lately federated distinct provinces, with conflicting interests arising
from difference of races, nationalities, and religions. PoHtical federation
is not new in the history of the world, though it generally arises as a
consequence of war. It was war that taught the Netherlands to federate
in 1619. It was war which united the States in America ; federated
Switzerland, Germany, and Austria, and unified Italy. But Canada
formed a great national life out of petty provincial existences in a time
of profound peace. This evolution gave an immense impulse to her
national resources. The Dominion still requires consolidation in its vast
extent, and applied science is rapidly effecting it. Canada, with its great
expanse of territory, nearly as large as the United States, is being knit
b2
4 REroTiT — 1885.
together by the iron bands of railways from the Gulf of St. Lawrence to
the Pacific Ocean, so that the fertile lands of Ontario, Manitoba, Columbia,
and the NorthTVestern Territories will soon be available to the world.
Still practical science has much to accomplish. England and France,
with only onefifth the fertile area of Canada, support 80 millions of
people, while Canada has a population not exceeding 5 millions.
A less farseeing people than the Canadians might have invited the
applied science which they so much require. But they knew that with
out science there are no applications. They no doubt felt with Emerson —
And what if Trade sow cities
Like shells along the shore,
And thatch with towns the prairie broad
With railwaj's ironed o'er ;
The}' are but sailing foambells
Along Thought's causing stream.
And take their shape and suncolour
From liim that sends the dream.
So it was with a farreaching foresight that the Canadian Government
invited the British Association for the Advancement of Science to meet
in Montreal. The inhabitants of Canada received us with open arms,
and the science of the Dominion and that of the United Kingdom were
welded. We found in Canada, as we had every reason to expect, men of
manly and selfreliant character who loved not less than we did the old
home from which they had come. Among them is the same healthi
ness of political and moral life, with the same love of truth which dis
tinguishes the English people. Our great men are their great men ; our
Shakspcare, Milton, and Burns belong to them as much as to ourselves ;
our Newton, Dalton, Faraday, and Darwin are their men of science as
much as they are ours. Thus a common possession and mutual sympathy
made the meeting in Canada a successful effort to stimulate the progress
of science, while it established, at the same time, the principle that all
people of British origin — and I would fain include our cousins in the
United States — possess a common interest in the intellectual glories of
their race, and ought, in science at least, to constitute part and parcel of
a common empire, whose heart may beat in the small islands of the
Northern seas, but whose blood circulates in all her limbs, carrying
warmth to them and bringing back vigour to us. Nothing can be more
cheering to our Association than to know that many of the young com
munities of Englishspeaking people all over the globe — in India, China,
Japan, the Straits, Ceylon, Australia, New Zealand, the Cape — have
founded scientific societies in order to promote the growth of scientific
research. No doubt science, which is only a form of truth, is one in all
lands, but still its unity of purpose and fulfilment received an important
practical expression by our visit to Canada. This community of science
will be continued by the fact that we have invited Sir William Dawson, .
of Montreal, to be our next President at Birmingham,
ADDRESS. O
II. Science and the State.
I cannot address you in Aberdeen without recollecting that when we
last met in this city our President was a great prince. The just verdict
of time is that, high as was his royal rank, he has a far nobler claim to
our regard as a lover of humanity in its widest sense, and especially as a
lover of those arts and sciences which do so much to adorn it. On
September 14, 1859, I sat on this platform and listened to the eloquent
address and wise counsel of the Prince Consort. At one time a member
of his household, it was my privilege to cooperate with this illustrious
prince in many questions relating to the advancement of science. I
naturally, therefore, turned to his presidential address to see whether I
might not now continue those counsels which he then gave with all the
breadth and comprehensiveness of his masterly speeches. I found, as I
expected, a text for my own discourse in some pregnant remarks which
he made upon the relation of Science to the State. They are as
follows : — 'We may be justified in hoping . . . that the Legislature and
the State will more and more recognise the claims of science to their
attention, so that it may no longer require the beggingbox, but speak to
the State like a favoured child to its parent, sure of his paternal solicitude
for its welfare ; that the State will recognise in science one of its elements
of strength and prosperity, to foster which the clearest dictates of self
interest demand.'
This opinion, in its broadest sense, means that the relations of science
to the State should be made more intimate because the advance of science
is needful to the public weal.
The importance of promoting science as a duty of statecraft was well
enough known to the ancients, especially to the Greeks and Arabs, but it
ceased to be recognised in the dark ages, and was lost to sight during the
revival of letters in the fifteenth and sixteenth centuries. Germany and
France, which are now in such active competition in promoting science,
have only publicly acknowledged its national importance in recent times.
Even in the last century, though France had its Lavoisier and Germany
its Leibnitz, their Governments did not know the value of science. When
the former was condemned to deatli in the Reign of Terror, a petition was
presented to the rulers that his life might be spared for a few weeks in
order that he might complete some important experiments, but the reply
was, ' The Republic has no need of savants.' Earlier in the century the
muchpraised Frederick William of Prussia shouted with a loud voice,
during a graduation ceremony in the University of Frankfort, ' An ounce
of motherwit is worth a ton of university wisdom.' Both France and
Germany are now ashamed of these utterances of their rulers, and make
energetic eflbrts to advance science with the aid of their national resources.
More remarkable is it to see a young nation like the United States reserv
ing large tracts of its national lands for the promotion of scientific
education. In some respects this young country is in advance of all
4 REPORT — 1885.
together by the iron bands of railways from the Gulf of St. Lawrence to
the PaciGc Ocean, so that the fertile lands of Ontario, Manitoba, Columbia,
and the North Western Territories will soon be available to the world.
Still practical science has much to accomplish. England and France,
with only onefifth the fertile area of Canada, support 80 millions of
people, while Canada has a population not exceeding 5 millions.
A less farseeing people than the Canadians might have invited the
applied science which they so much require. But they knew that with
out science there are no applications. They no doubt felt with Emerson —
And what if Trade sow cities
Like shells along the shore,
And thatch with towns the prairie broad
M'ith railways ironed o'er ;
They are but sailing foambells
Along Thought's causing stream,
And take their shape and suncolour
Yiom him that sends the dream.
So it was with a farreaching foresight that the Canadian Government
invited the British Association for the Advancement of Science to meet
in Montreal. The inhabitants of Canada received us with open arms,
and the science of the Dominion and that of the United Kingdom were
welded. We found in Canada, as Ave had every reason to expect, men of
manly and selfreliant character who loved not less than we did the old
home from whicli they had come. Among them is the same healthi
ness of political and moral life, with the same love of truth which dis
tinguishes the English people. Our great men are their great men ; our
Shakspcare, !Milton, and Burns belong to them as much as to ourselves ;
our Newton, Dalton, Faraday, and Darwin are their men of science as
much as they are ours. Thus a common possession and mutual sympathy
made the meeting in Canada a successful effort to stimulate the progress
of science, while it established, at the same time, the principle that all
people of British origin — and I would fain include our cousins in the
United States — possess a common interest in the intellectual glories of
their race, and ought, in science at least, to constitute part and parcel of
a common empire, whose heart may beat in the small islands of the
Northern seas, but whose blood circulates in all her limbs, carrying
warmth to them and bringing back vigour to us. Nothing can be more
cheering to our Association than to know that many of the young com
munities of Englishspeaking people all over the globe — in India, China,
Japan, the Straits, Ceylon, Australia, New Zealand, the Cape — have
founded scientific societies in order to promote the growth of scientific
research. No doubt science, which is only a form of truth, is one in all
lands, but still its unity of purpose and fulfilment received an important
practical expression by our visit to Canada. This community of science
will be continued by the fact that we have invited Sir William Dawson,
of Montreal, to be our next President at Birmingham.
ADDRESS. O
II. Science and the State.
1 cannot address you in Aberdeen without recollecting that when we
last met in this city our President was a great prince. The just verdict
of time is that, high as was his royal iank, he has a far nobler claim to
our regard as a lover of humanity in its widest sense, and especially as a
lover of those arts and sciences which do so much to adorn it. On
September 14, 1859, I sat on this platform and listened to the eloquent
address and wise counsel of the Prince Consort. At one time a member
of his household, it was my privilege to cooperate with this illustrious
prince in many questions relating to the advancement of science. I
naturally, therefoi'e, turned to his presidential address to see whether I
might not now continue those counsels which he then gave with all the
breadth and comprehensiveness of his masterly speeches. I found, as I
expected, a text for my own discourse in some pregnant remarks which
he made upon the relation of Science to the State. They are as
follows : — 'We may be justified in hoping . . . that the Legislature and
the State will more and more recognise the claims of science to their
attention, so that it may no longer require the beggingbox, but speak to
the State like a favoured child to its parent, sure of his paternal solicitude
for its welfare ; that the State will recognise in science one of its elements
of strength and prosperity, to foster which the clearest dictates of self
interest demand.'
This opinion, in its broadest sense, means that the relations of science
to the State should be made more intimate because the advance of science
is needful to the public weal.
The importance of promoting science as a duty of statecraft was well
enough known to the ancients, especially to the Greeks and Arabs, but it
ceased to be recosjuised in the dark a^es, and was lost to sigrht during the
revival of letters in the fifteenth and sixteenth centuries. Germany and
France, which are now in such active competition in promoting science,
have only publicly acknowledged its national importance in recent times.
Even in the last century, though France had its Lavoisier and Germany
its Leibnitz, their Governments did not know the value of science. When
the former was condemned to deatli in the Reign of Terror, a petition was
presented to the rulers that his life might be spared for a few weeks in
order that he might complete some important experiments, but the reply
was, ' The Republic has no need of savants.' Earlier in the century the
muchpraised Frederick William of Prussia shouted with a loud voice,
during a graduation ceremony in the University of Frankfort, ' An ounce
of motherwit is worth a ton of university wisdom.' Both France and
Germany are now ashamed of these utterances of their rulers, and make
energetic efforts to advance science with the aid of their national resources.
More remarkable is it to see a young nation like the United States reserv
ing large tracts of its national lands for the promotion of scientific
education. In some respects this young country is in advance of all
6 ■ EEPORT 1885.
Europoan nations in joining science to its administrative offices. Its
scientific publications, like the great palteontological work embodying
the researches of Professor Marsh and his associates in the Geological
Survey, are an example to other Governments. The Minister of Agricul
ture is surrounded with a staff of botanists and chemists. The Home
Secretary is aided by a special Scientific Commission to investigate the
habits, migrations, and food of fishes, and the latter has at its disposal two
speciallyconstrncted steamers of large tonnage. The United States and
Gi'eat Britain i^iomote fisheries on distinct systems. In this country we
are perpetually issuing expensive Commissions to visit the coasts in order
to ascertain the experiences of fishermen. I have acted as Chairman of one
of these Royal Commissions, and found that the fishermen, having only a
knowledge of a small area, gave the most contradictory and unsatisfactory
evidence. In America the questions are put to Nature, and not to fisher
men. Exact and searching investigations are made into the lifehistory
of the fishes, into the temperature of the sea in which they live and
spawn, into the nature of their food, and into the habits of their natural
enemies. For this purpose the Government give the cooperation of the
navy, and provide the Commission with a special corps of skilled naturalists,
some of whom go out with the steamships and others work in the
biological laboratories at Wood's Holl, Massachusetts, or at Washington.
The difierent universities send their best naturalists to aid in these in
vestigations, which are under the direction of Mr. Baird, of the Smith
sonian Institution. The annual cost of the Federal Commission is about
40,000/., while the separate States spend about 2O,O00Z. in local efibrts.
The practical results flowing from these scientific investigations have
been important. The inland waters and rivers have been stocked with
fish of the best and most suitable kinds. Even the great ocean which
washes the coasts of the United States is beginning to be afiected by the
knowledge thus acquired, and a sensible result is already produced upon
the most important of its fisheries. The United Kingdom largely depends
upon its fisheries, but as jet our Government have scarcely realised the
value of such scientific investigations as those pursued with success by
the United States. Less systematical!}', but with great benefit to science,
our own Government has used the surveying expeditions, and sometimes
has ec^uipped special expeditions to promote natural history and solar
physics. Some of the latter, like the voyage of the ' Challenger,' have
added largely to the store of knowledge ; while the former, though not
primarily intended for scientific research, have had an indirect result
of infinite value by becoming trainingschools for such investigators
as Edward Forbes, Darwin, Hooker, Huxley, Wyville Thomson, and
others.
In the United Kingdom we are just beginning to understand the
wisdom of Washington's farewell address to his countrymen, when he said :
' Promote as an object of primary importance institutions for the general
diffusion of knowledge. In proportion as the structure of a governmeafc
ADDRESS. 7
gives force to public opinion, it is essential that public opinion should be
enlightened.' It was only in 1870 that our Parliament established a
system of national primary education. Secondary education is chaotic,
and remains unconnected with the State, while the higher education of
the universities is only brought at distant intervals under the view of the
State. All great countries except England have Ministers of Education,
but this country has only Ministers who are the managers of primary
schools. We are inferior even to smaller countries in the absence of
organised State supervision of education. Greece, Portugal, Egypt, and
Japan have distinct Ministers of Education, and so also among our
Colonies have Victoria and New Zealand . Gradually England is gathering
materials for the establishment of an efficient Education Minister. The
Department of Science and Art is doing excellent work in diffusino
a taste for elementary science among the working classes. There are
now about 78,000 persons who annually come under the influence of its
science classes, while a small number of about two hundied, many of them
teachers, receive thorough instruction i"n science at the excellent school
in South Kensington of which Professor Huxley is the Dean. I do not
dwell on the work of this Government department, because my object ia
chiefly to point out how it is that science lags in its progress in the United
Kingdom owing to the deficient interest taken in it hj the middle and
upper classes. The working classes are being roused from their indifi'er
ence. They show this by their selection of scientific men as candidates at
the next election. Among these are Professors Stuart, Roscoe, Maskelyne,
and Riicker. It has its significance that such a humble representative of
science as myself received invitations from workingclass constituencies
in more than a dozen of the leading manufacturing towns. In the next
Parliament I do not doubt that a Minister of Education will be created
as a nucleus round which the various educational materials may crystallise
in a definite form.
III. Science and Secondary Education.
Various Royal Commissions have made inquiries and issued recom
mendations in regard to our public and endowed schools. The Com
missions of I86I, 1804, 1868, and 1873 have expressed the strongest
disapproval of the condition of our schools, and, so far as science is
concerned, their state is much the same as when the Duke of Devon
shire's Commission in 1873 reported in the following words : — ' Con
sidering the increasing importance of science to the material interests of
the country, we cannot but regard its almost total exclusion from the
training of the upper and middle classes as little less than a national mis
fortune.' No doubt there are exceptional cases and some brilliant examples
of improvement since these words were written, but generally throughout
the country teaching in science is a name rather than a reality. The
Technical Commission which reported last year can only point to three
schools in Great Britain in which science is fully and adequately taught.
8 REPORT 1885.
While tbe Commission gives ns the consolation that England is still in
advance as an industrial nation, it warns us that foreign nations, which
were not long ago far behind, are now making more rapid progress than
this country, and will soon pass it in the race of competition unless we
give increased attention to science in public education. A few of the
large towns, notably Manchester, Bradford, Hnddersfield, and Birming
ham, are doing so. The working classes are now receiving better
instruction in science than the middle classes. The competition of
actual life asserts its own conditions, for the children of the latter 6nd
inci'easing difficulty in obtaining emjiloyment. The cause of this lies in
the fact that the schools for the middle classes have not yet adapted
themselves to tbe needs of modern life. It is true that many of the
endowed schools have been put under new schemes, but as there is no
public supervision or inspection of them, we have no knowledge as to
whether they have prospered or slipped back. Many corporate schools
have arisen, some of them, like Clifton, Cheltenham, and Marlborough
Colleges, doing excellent educational work, though as regards all of them
the public have no rights and cannot enforce guarantees for efficiency.
A Return just issued, on the motion of Sir John Lubbock, shows a
lamentable deficiency in science teaching in a great proportion of the
endowed schools. While twelve to sixteen hours per week ars devoted to
classics, two to three hours are considered ample for science in a large
proportion of the schools. In Scotland there are only six schools in the
Return which give more than two hours to science weekly, while in many
schools its teaching is wholly omitted. Every other part of the kingdom
stands in a better position than Scotland in relation to the science of its
endowed schools. The old traditions of education stick as firmly to
schools as a limpet does to a rock ; though I do the limpet injustice, for
it does make excursions to seek pastuies new. Are we to give up in
despair because an exclusive system of classical education has resisted
the assatilts of such cultivated authors as Milton, Montaigne, Cowley, and
Locke ? There was once an enlightened Emperor of China, Chi Hwangti,
who knew that his country was kept back by its exclusive devotion to the
classics of Confucius and Mencius. He invited 500 of the teachers to
bring their copies of these authors to Pekin, and after giving a great
banquet in their honour, he buried alive the professors along with
their manuscripts in a deep pit. But Confucius and j\Ienciu8 still reign
supreme. I advocate milder measures, and depend for their adoption on
the force of public opinion. The needs of modern life will force schools
to adapt themselves to a scientific age. Grammarschools believe them
selves to be immortal. Those curious immortals — the Struldbrugs —
described by Swift, ultimately regretted their immortality, because they
found themselves out of touch, sympathy, and fitness with the centuries
in which they lived.
As there is no use clamouring for an instrument of more compass and
power until we have made up our mind as to the tune, Pi'ofessor Huxley, in
ADDRESS. 9
his evidence before a Parliamentary Committee in 1884, has given a time
table for grammarschools. He demands that out of their forty hours
for public and private study, ten should be given to modern languages and
history, eight to arithmetic and mathematics, six to science, and two to
geography, thus leaving fourteen hours to the dead languages. No time
table would, however, be suitable to all schools. The great public schools
of England will continue to be the gymnasia for the upper classes, and
should devote much of their time to classical and literary culture. Even
now they introduce into their curriculum subjects unknown to them
when the Royal Commission of 18G8 reported, though they still accept
science with timidity. Unfortunately, the other grammarschools which
educate the middle classes look to the higher public schools as a type to
which they should conform, although their functions are so different.
It is in the interest of the higher public schools that this difference
should be recognised, so that, while they give an allround education and
expand their curriculum by a freer recognition of the value of science as
an educational power in developing the faculties of the upper classes,
the schools for the middle classes should adapt themselves to the needs
of their existence, and not keep up a slavish imitation of schools with a
different function.
The stock argument against the introduction of modern subjects into
grammarschools is that it is better to teach Latin and Greek thoroughly
rather than various subjects less completely. But is it true that
thoroughness in teaching dead languages is the result of an exclusive
system ? In 1868 the Royal Commission stated that even in the few
great public schools thoroughness was only given to thirty per cent, of
the scholars, at the sacrifice of seventy per cent, who got little benefit
from the system. Since then the curriculum has been widened and the
teaching has improved. I question the soundness of the principle that it
is better to limit the attention of the pupils mainly to Latin and Gi'eek,
highly as I value their educational power to a certain order of minds.
As in biology the bodily development of animals is from the general to
the special, so is it in the mental development of man. In the school a
boy should be aided to discover the class of knowledge that is best suited
for his mental capacities, so that, in the upper forms of the school and in the
university, knowledge maybe specialised in order to cultivate the powers
of the man to their fullest extent. Shakspeare's educational formula
may not be altogether true, but it contains a broad basis of truth —
No profit grows, where is no pleasure ta'en ; —
In brief, sii', study what you most affect.
The comparative failure of the modern side of school education arises
from constituting it out of the boys who are looked upon as classical
asses. Milton pointed out that in all schools there are boys to whom the
dead languages are ' like thorns and thistles,' which form a poor nourish,
ment even for asses. If teachers looked upon these classical asses as
beings who might receive mental nurture according to their nature,
]0 REPORT — 1885.
mucli higher results ■would follow the bifurcation of our schools. Saul
•went out to look for asses and he found a kingdom. Surely this fact
is more encouraging than the. example of Gideon, who ' took thorns of
the wilderness and briars, and with these he taught the men of Succoth.' '
The adaptation of public schools to a scientific age does not involve
a contest as to whether science or classics shall prevail, for both are
indispensable to true education. The real question is whether schools
will undertake the duty of moulding the minds of boys according to their
mental varieties. Classics, from their structural perfection and power of
awakening dormant faculties, have claims to precedence in education,
but they have none to a practical monopoly. It is by claiming the latter
that teachers sacrifice mental recepti^ity to a Procrustean uniformity.
The universities are changing their traditions more rapidly than the
schools. The via antiqua which leads to them is still broad, though a
via moderna, with branching avenues, is also open to their honours and
emoluments. Physical science, which was once neglected, is now
encouraged at the universities. As to the seventy per cent, of boys who
leave schools for lifework without going through the universities, are
there no growing signs of discontent which must force a change ? The
Civil Sei'vice, the learned professions, as well as the armj^ and navy, are
now barred by examinations. Do the boys of our public schools easily
leap over the bars, although some of them have lately been lowered so as
to suit the schools ? So difficult are these bars to scholars that crammers
take them in hand before they attempt the leap ; and this occurs in spite
of the large value attached to the dead languages and the small value
placed on modern subjects. Thus, in the Indian Civil Service examina
tions, SOO marks as a maximum are assigned to Latin, GOO to Greek, 500
to chemistry, and 300 to each of the other physical sciences. But if we
take the average working of the system for the last four years, we find
that while sixtyeight per cent, of the maximum were given to candidates
in Greek and Latin, only fortyfive pen' cent, were accorded to candidates in
chemistry, and but thirty per cent, to the other physical sciences. Schools
sending up boys for competition naturally shun subjects which are dealt
"with so hardly and so heavily handicapped by the State.
Passing from learned or public professions to commerce, how is it
that in our great commercial centres, foreigners — German, Swiss, Dutch,
and even Greeks — push aside our English youth and take the places of
profit which belong to them by national inheritance ? How is it that in
our Colonies, like those in South Africa, German enterprise is pushing
aside English incapacity ? How is it that we find whole branches of
manufactures, when they depend on scientific knowledge, passing away
from this country, in which they originated, in order to engraft themselves
abroad, although their decaying roots remain at home ?  The answer to
' Judges viii. IG.
 See Dr. Perkin.s' address to the Soc. Chem. Industry. 'Nature,' Aug. 6, 1885,
p. 333.
ADDRESS. 1 1
tliese questions is that our systems of education are still too narrow for
the increasing struggle of life.
Faraday, who had no narrow vie\YS in regard to education, deplored
the future of our youth in the competition of the world, because, as he
said with sadness, ' our schoolboys, when they come out of school, are
isrnorant of their ignorance at the end of all that education.'
The opponents of science education allege that it is not adapted for
mental development, because scientific facts are often disjointed and
exercise only the memory. Those who argue thus do not know what
science is. No doubt an ignorant or halfinformed teacher may present
science as an accumulation of unconnected facts. At all times and in all
subjects there are teachers without a3sthetical or philosophical capacity
— men who can only see carbonate of lime in a statue by Phidias or
Praxiteles ; who cannot survey zoology on account of its millions of
species, or botany because of its 130,000 distinct plants ; men who can look
at trees without getting a conception of a forest, and cannot distinguish a
stately edifice from its bricks. To teach in that fashion is like going to
the tree of science with its glorious fruit in order to pick up a handful of
the dry fallen leaves from the ground. It is, however, true that as
science teaching has had less lengthened experience than that of literature,
its methods of instruction are not so matured. Scientific and literary
teaching have difiierent methods ; for while the teacher of literature rests
on authority and on books for his guidance, the teacher of science
discards authority and depends on facts at first hand, and on the book of
Nature for their interpretation. Natural science more and more resolves
itself into the teaching of the laboratory. In this way it can be used as
a powerful means of quickening observation, and of creating a faculty of
induction after the manner of Zadig, the Babylonian described by
Voltaire. Thus facts become surrounded by scientific conceptions, and
are subordinated to order and law.
It is not those who desire to unite literature with science who degrade
education ; the degradation is the consequence of the refusal. A violent
reaction — too violent to be wise — has lately taken place against classical
education in France, where their own vernacular occupies the position of
dead languages, while Latin and science are given the same time in the
curriculum. In England manufacturers cry out for technical education,
in which classical culture shall be excluded. In the schools of the middle
classes science rather than technics is needed, because, when the seeds of
science are sown, technics as its fruit will appear at the appointed time.
Epictetus was wise when he told us to observe that, though sheep eat
grass, it is not grass but wool that grows on their backs. Should, how
ever, our grammarschools persist in their refusal to adapt themselves to
the needs of a scientific age, England must follow the example of other
European nations and found new modern schools in competition with
them. For, as Huxley has put it, we cannot continue in this age ' of full
modern artillery to turn out our boys to do battle in it, equipped only
12 KEPOET — 1885.
with the sword and shield of an ancient gladiator.' In a scientific and
keenly competitive age an exclusive education in the dead languages is
a perplexing anomaly. The flowers of literature should be cultivated and
gathered, though it is not wise to send men into our fields of industry to
gather the harvest when they have been taught only to cull the poppies
and to push aside the wheat.
IV. Science and the Universities.
The Stale has always felt bound to alter and improve universities,
even when their endowments are so large as to render it unnecessary to
support them by public funds. When universities are poor, Parliament
gives aid to them from imperial taxation. In this country that aid has
been given with a very spaiing hand. Thus the universities and colleges
of Ireland have received about thirty thousand pounds annually, and tbo
same sum has been granted to the four universities of Scotland. Com
pared Avith imperial aid to foreign universities such sums are small. A
single German university like Strasburg or Leipsic receives above
40,000Z. annually, or 10,000/. more than the whole colleges of Ireland or
of Scotland. Strasburg, for instance, has had her university and its
libraiy rebuilt at a cost of 711,000Z., and receives an annual subscription
of 43,000Z. In rebuilding the university of Strasburg eight laboratories
have been provided, so as to equip it fully with the modern requirements
for teaching and reseai'ch.' Prussia, the most economical nation in the
world, spends 391,000/. yearly out of taxation on her universities.
The recent action of France is still more remarkable. After the
FrancoGerman War the Institute of France discussed the important
question : — ' Poui'quoi la France n'a pas trouve d'hommes superieurs au
moment du \)(:v\\ ? ' The general answer was because France had allowed
university education to sink to a low ebb. Before the great Revolution
France had twentythi'ee autonomous universities in the provinces.
Xapoleon desired to found one great university at Paris, and he crushed
out the others with the hand of a despot, and remodelled the last with the
instincts of a drillsergeant. The central university sank so low that in
1868 it is said that only 8,000/. were spent for true academic purposes.
Startled by the intellectual sterility shown in the war, France has made
gigantic eiforts to retrieve her position, and has rebuilt the provincial
colleges at a cost of 3,280,000/., while her annual budget for their support
now reaches half a million of pounds. In order to open these provincial
colleges to the best talent of France, more than five hundred scholarships
have been founded at an annual cost of 30,000/. France now recognises that
it is not by the number of men under arms that she can compete with her
great neighbour Germany, so she has determined to equal her in intellect.
' The cost of these laboratories has been as follows : — Chemical Institute, 35,000Z. ;
Physical Institute, 28,000Z. ; Botanical Institute, 2G,000Z. ; Observatory, 25,000?. ;
Anatomy, 42,000/.; Clinical Surgery, 26,000/.; Physiological Chemistry, 16,000/.;
Physiological Institute, 13,900/,
ADDRESS. 13
Tou will understand why it is that Germany was obliged, even if slie had
not been willing, to spend sach large sums in order to equip the university
of her conquered province, Alsace Lorraine. France and Germany are
fully aware that science is the source of wealth and power, and that the
only way of advancing it is to encourage universities to make researches
and to spread existing knowledge through the community. Other
European nations are advancing on the same lines. Switzerland is a
remarkable illustration of how a country can compensate itself for its
natural disadvantages by a scientific education of its people. Switzerland
contains neither coal nor the ordinary raw materials of industry, and is
separated from other countries which might supply them by mountain
barriers. Yet, by a singularly good system of graded schools, and by the
great technical college of Ziirich, she has become a prosperous manufac
turing country. In Great Britain we have nothing comparable to thia
technical college, either in magnitude or efScieucy. Belgium is reor
ganising its universities, and the State has freed the localities from the
charge of buildings, and will in future equip the universities with efficient
teaching resources out of public taxation. Holland, with a population of
4,000,000 and a small revenue of 9,000,000/., spends 13G,O0OZ. on her
four universities. Contrast this liberality of foreign countries in the
promotion of higher instruction with the action of our own country.
Scotland, like Holland, has four universities, and is not very different
from it in population, but it only receives 30,000/. from the Slate. By a
special clause in the Scotch Universities Bill the Governm_ent asked
Parliament to declare that under no circumstances should the Parlia
mentary grant be ever increased above 40,000?. According to the views
of the British Treasury there is a finality in science and in expandino
knowledge.
The wealthy universities of Oxford and Cambridge are gradually con
structing laboratories for science. The merchant princes of Manchester
have equipped their new Victoria University with similar laboratories.
Edinburgh and Glasgow Universities have also done so, partly at the
cost of Government and largely by private subscriptions. The poorer
universities of Aberdeen and St. Andrews are still inefficiently provided
with the modern appliances for teaching science.
London has one small Government college and two chartered colleoes,
but is wholly destitute of a teaching university. It would excite oreat
astonishment at the Treasury if we were to make the modest request that
the great metropolis, with a population of four millions, should be put
into as efficient academical position as the town of Strasburg, with
104,000 inhabitants, by receiving, as that town does, 43,000/. annually for
academic instruction, and 700,000/. for university buildings. Still, the
amazing anomaly that London has no teaching university must ere long
cease.
It is a comforting fact that, in spite of the indifference of Parliament,
the large towns of the kingdom are showing their sense of the need of
14 EEPOET — 1885.
higher education. Manchester has already its university. Nottingham,
Birmingham, Leeds, and Bristol have colleges more or less complete.
Liverpool converts a disused lunatic asylum into a college for sane people.
Cardiff rents an infirmary for a collegiate building. Dundee, by private
benefaction, rears a Baxter College with larger ambitions. All these
are healthy signs that the public are determined to have advanced science
teachinc ; but the resources of the institutions are altogether inadequate
to the end in view. Even in the few cases where the laboratories are effi
cient for teachino purposes, they are inefficient as laboratories for research.
Under these circumstances the Royal Commission on Science advocates
special Government laboratories for research. Such laboratories, sup
ported by public money, are as legitimate subjects for expenditure as
"alleries for pictures or sculpture ; but I think that they would not be
successful, and would injure science if they failed. It would be safer in
the meantime if the State assisted universities or wellestablished colleges
to found laboratories of research under their own care. Even such a
proposal shocks our Chancellor of the Exchequer, who tells us that this
country is burdened with public debt, and has ironclads to build and
arsenals to provide. Nevertheless our wealth is proportionally much
greater than that of foreign States which are competing with so much
vigour in the promotion of higher education. They deem such expenditure
to be true economy, and do not allow their huge standing armies to be
an apology for keeping their people backwards in the march of knowledge.
France, which in the last ten years has been spending a million annually
on university education, had a war indemnity to pay, and competes suc
cessfully with this country in ironclads. Either all foreign States are
stranoely deceived in their belief that the competition of the world has
become a competition of intellect, or we are marvellously unobservant of J
the change which is passing over Europe in the higher education of the ^
people. Preparations for war will not ensure to us the blessings and 
security of an enlightened peace. Protective expenditure may be wise,
thongh productive expenditure is wiser.
Were half the powers which fill the worlrl with terror,
AVere half the wealth bestowed on camps and courts,
Given to redeem the human mind from error^
There were no need of arsenals and forts.
Universities are not mere storehouses of knowledge ; they are also
conservatories for its cultivation. In Mexico there is a species of ant which
sets apart some of its individuals to act as honeyjars by monstrously
extending their abdomens to store the precious fluid till it is wanted
by the community. Professors in a university have a higher function,
because they ought to make new honey as well as to store it. The
widening of the bounds of knowledge, literary or scientific, is the crown
ino olory of university life. Germany unites the functions of teaching
and research in the universities, while France keeps them in separate
institutions. The former system is best adapted to our habits, but its
ADDRESS. 15
condition for success is tliafc our science chairs should be greatly increased,
so that teachers should not be wholly absorbed in the duties of instruc
tion. Germany subdivides the sciences into various chairs, and gives to
the professors special laboratories. It also makes it a condition for the
higher honours of a university that the candidates shall give proofs cf
their ability to make original researches. Under such a system, teaching
and investigation are not incompatible. In the evidence before the
Science Commission many opinions were given that scientific men en
gaged in research should not be burdened with the duties of education,
and there is much to be said in support of this view when a sinole
professor for the whole range of a physical science is its only represen
tative in a university. But I hope that such a system will not long
continue, for if it do we must occupy a very inferiar position as a nation
in the intellectual competition of Europe. Research and education in
limited branches of higher knowledge are not incompatible. It is true
that Gahleo complained of the burden imposed upon him by his numerous
astronomical pupils, though few other philosophers have echoed this com
plaint. Newton, who produced order in worlds, and Dalton, who brought
atoms under the reign of order and number, rejoiced in their pupils.
Lalande spread astronomers as Liebig spread chemists, and Johannes
Miiller biologists, all over the world. Laplace, La Grange, Dulong,
Gay Lussac, Berthollet, and Dumas were professors as well as discoverers
in France. In England our discoverers have generally been teachers.
In fact I recollect only three notable examples of men who were not —
Boyle, Cavendish, and Joule. It was so in ancient as well as in modern
times, for Plato and Aristotle taught and philosophised. If you do not
make the investigator a schoolmaster, as Dalton was, and as practically
our professors are at the present time, with the duty of teaching all
branches of their sciences, the mere elementary truths as well as the
highest generalisations being compressed into a course, ifc is well that
they should be brought into contact with the world in which they live,
so as to know its wants and aspirations. They could then quicken the
pregnant minds around them, and extend to others their own power and
love of research. Goethe had a fine perception of this when he wrote —
Wer in cTer Weltgeschichte lebt,
Wer in die Zeiten schaut, und strebt,
Nur der ist werth, zu sprechen und zu dichtcn.
Our universities are still far from the attainment of a proper com
bination of their resources between teaching and research. Even Oxford
and Cambridge, which have done so much in recent years in the equip
ment of laboratories and in adding to their scientific stafP, are still far
behind a secondclass German university. The professional faculties of
the English universities are growing, and will dififuse a greater taste for
science among their students, though they may absorb the time of the
limited professoriate so as to prevent it advancing the boundaries of
16 REPORT — 1885.
knowledoe. Professional faculties are absolutely essential to tbe existence
of universities in poor countries like Scotland and Ireland. This L.is
been the case from the early days of the Bologna University up to the
present time. Originally universities arose not by mere bulls of popes,
but as a response to the strong desire of the professional classes to dignify
their crafts by real knowledge. If their education had been limited to
mere technical schools like the Medical School of Salerno which flourished
in the eleventh century, length but not breadth would have been given to
education. So the universities wisely joined culture to the professional
ociences. Poor countries like Scotland and Ireland must have their
academic systems based on the professional faculties, although wealthy
universities like Oxford and Cambridge may continue to have them as
mere supplements to a more general education. A greater liberality
of support on the part of the State in the establishment of chairs of
science, for the sake of science and not merely for the teaching of the
professions, would enable the poorer universities to take their part in the
advancement of knowledge.
I have already alluded to the foundation of new colleges in different
parts of the kingdom. Owens College has worthily developed into the
Victoria University. Formerly she depended for degrees on the
University of London. No longer will she be like a moon reflecting cold
and sickly rays from a distant luminary, for in future she will be a sun,
a centre of intelligence, warming and illuminating the regions around her.
The other colleges which have formed themselves in large manufacturing
districts are remarkable expressions from them that science must be
promoted. Including the colleges of a high class, such as University
College and King's College in London, and the three Queen's Colleges in
Ireland, the aggregate attendance of students in colleges without university
rank is between nine and ten thousand, while that of the universities is
fifteen thousand. No doubt some of the provincial colleges require
considerable improvement in their teaching methods; sometimes they
unwisely aim at a full university curriculum when it would be better for
them to act as faculties. Still they are all growing in the spirit of self
help, and some of them are destined, like Owens College, to develop into
universities. This is not a subject of alarm to lovers of education,
while it is one of hope and encouragement to the great centres of
industry. There are too few autonomous universities in England in
proportion to its population. "While Scotland, with a population
of 3J millions, has four universities with 6,500 students, England,
with 26 millions of people, has only the same number of teaching
universities with 6,000 students. Unless English colleges have such
ambition, they may be turned into mere mills to grind out material for
examinations and competitions. Higher colleges should always hold
before their students that knowledge, for its own sake, is the only object
worthy of reverence. Beyond college life there is a land of research
flowing with milk and honey for those who know how to cultivate it.
ADDRESS. 1 1
Colleges should at least show a Pisgah view of this Land of Promise,
which stretches far beyond the Jordan of examinations and competitions.
V. Science and Inclustnj,
In the popular mind the value of science is measured by its applica
tions to the useful purposes of life. It is no doubt true that science
wears a beautiful aspect when she confers practical benefits upon man.
But truer relations of science to industry are implied in Greek mythology.
Vulcan, the god of industry, wooed science, in the form of Minerva, with
a passionate love, but the chaste goddess never married, although she
conferi'ed upon mankind nearly as many arts as Prometheus, who, like
other inventors, saw civilisation progressing by their use while he lay
groaning in want on Mount Caucasus. The rapid development of industry
in modern days depends on the applications of scientific knowledge,
while its slower growth in former times was due to experiments being
made by trial and error in order to gratify the needs of man. Then an
experiment was less a questioning of Nature than an exercise on the mind
of the experimentalist. For a true questioning of Nature only arises when
intellectual conceptions of the causes of phenomena attach themselves to
ascertained facts as well as to their natural environments. Much real
science had at one time accumulated in Egypt, Greece, Rome, and Arabia,
though it became obscured by the intellectual darkness which spread
over Europe like a pall for many centuries. The mental results of Greek
science, filtered through the Romans and Arabians, gradually fertilised
the soil of Europe. Even in ages which are deemed to be dark and un
prolific, substantial though slow progress was made. By the end of the
fifteenth century the mathematics of the Alexandrian school had become
the possession of Western Europe ; Arabic numerals, algebra, trigo
nometry, decimal reckoning, and an improved calendar having been
added to its stock of knowledgre. The old discoveries of Democritus and
Archimedes in physics, and of Hipparchus and Ptolemy in astronomy,
were producing their natural developments, though with great slowness.
Many manufactui'es, growing chiefly by experience, and occasionally
lightened up by glimmerings of science throughout the prevailing dark
ness, had arisen before the sixteenth century. A knowledge of the pro
perties of bodies, though scarcely of their relations to each other, came
through the labours of the alchemists, who had a mighty impulse to
work, for by the philosopher's stone, often not larger than half a rape
seed, they hoped to attain the three sensuous conditions of human enjoy
ment, gold, health, and immortality. By the end of the fifteenth century
many important manufactures were founded by empirical experiment,
with only the uncertain guidance of science. Among these were the
compass, printing, paper, gunpowder, guns, watches, forks, knitting
needles, horseshoes, bells, wood cutting and copper engraving, wire
drawing, steel, table glass, spectacles, micioscopes, glass mirrors backed
by amalgams of tin and lead, windmills, crushing and saw mills. These
1885. c
18 REPora — 1835.
important manufactures arose from an increased knowledge of facts,
around whicli scientific conceptions were slowly concreting. Aristotle
defines this as science when he says, ' Art begins when, from a great
number of experiences, one genei'al conception is formed which will
embrace all similar cases.' Such conceptions are formed only when
culture develops the human mind and compels it to give a rational
account of the world in which man lives, and of the objects in and around
it, as well as of the phenomena which govern their action and evolution.
Though the accumulation of facts is indispensable to the growtb of science,
a thousand facts are of less value to human progress than is a single one
when it is scientifically comprehended, for it then becomes generalised in all
similar cases. Isolated facts may be viewed as the dust of science. The dust
which floats in the atmosphere is to the common observer mere incoherent
matter in a wrong place, while to the man of science it is allimportant
when the rays of heat and light act upon its floating particles. It is by
them that clouds and rains are influenced ; it is by their selective influence
on the solar waves that the blue of the heavens and the beauteous colours
of the sky glorify all Nature. So, also, ascertained though isolated facts,
forming the dust of science, become th.e reflecting media of the light of
knowledge, and cause all Nature to assume a new a.spect. It is with the
light of knowledge that we are enabled to question Nature through direct
experiment. The hypothesis or theory which induces us to put tlie ex
perimental question maybe right or wrong; still, ^)?(c?e>is qiiestio dimidium
scienticB est — it is half way to knowledge when you know what you have
to inquire. Davy described hypothesis as the mere scafiblding of science,
useful to build up true knowledge, but capable of being put up or taken
down at pleasure. Undoubtedly a theory is only temporary, and the
reason is, as Bacon has said, that the man of science ' loveth truth more
than his theory.' The changing theories which the world despises are
the leaves of the tree of science drawing nutriment to the parent stems,
and enabling it to put forth new branches and to produce f I'uit ; and
though the leaves fall and decay, the very products of decay nourish the
roots of the tree and reappear in the new leaves or theories which succeed.
When the questioning of Nature by intelligent experiment has raised
a system of science, then those men who desire to apply it to industrial
inventions proceed by the same methods to make rapid progress in the
arts. They also must have means to compel Nature to reveal her secrets,
^neas succeeded in his great enterprise by plucking a golden branch
from the tree of science. Armed with this even dread Charon dared not
refuse a passage across the Styx ; and the gate of the Elysian fields was
unbarred when he hung the branch on its portal. Then new aspects of
Nature were revealed —
Another sun and stars they know
That shine like ours, but shine below.
It is by carrying such a golden branch from the tree of science that in
ADDEESS. 1 9
rentors are able to advance the arts. In illustration of bow slowly at
first and bow rapidly afterwards science and its applications arise, I will
take only two out of thousands of examples which lie ready to my hand.
One of the most familiar instances is air, for that surely should have been
soon understood if man's unaided senses are sufficient for knowledge. Air
has been under the notice of mankind ever since the first man drew bis
first breath. It meets him at every turn ; it fans him with gentle breezes,
and it buffets him with storms. And yet it is certain that this familiar
object — air — is very imperfectly understood up to the present time. We
now know by recent researches that air can be liquefied by pressure and
cold ; but as a child still looks upon air as nothing, so did man in his
early state. A vessel filled with air was deemed to be empty. But man,
as soon as he began to speculate, felt the importance of air, and deemed
it to be a soul of the world upon which the respiration of man and the
godlike quality of fire depended. Yet a really intelligent conception of
these two essential conditions to man's existence — respiration and com
bustion — was not formed till about a century ago (1 775). No doubt long
before that time there had been abundant speculations regarding air.
Anaximenes, 548 years before Christ, and Diogenes of Apollonia, a century
later, studied the properties of air so far as their senses would allow them ;
so, in fact, did Aristotle. Actual scientific experiments were made on air
about the year 1100 by a remarkable Saracen, Alhazen, who ascertained
important truths which enabled Galileo, Torricelli, Otto de Guericke, and
others at a later period to discover laws leading to important practical
applications. Still there was no intelligent conception as to the compo
sition of air until Priestley in 1774 i*epeated, with the light of science, an
empirical observation which Eck de Sulbach had made three hundred
years before upon the union of mercury with an ingredient of air and the
decomposition of this compound by heat. This experiment now proved
that the active element in air is oxygen. From that date our knowledge,
derived from an intelligent questioning of air by direct experiments, has
gone on by leaps and bounds. The air, which mainly consists of nitrogen
and oxygen, is now known to contain carbonic acid, ammonia, nitric acid,
ozone, besides hosts of living organisms which have a vast influence for
good or evil in the economy of the world. These microorganisms, the
latest contribution to our knowledge of air, perform great analytical
functions in organic nature, and are the means of converting much of its
potential energy into actual energy. Through their action on dead matter
the mutual dependence of plants and animals is secured, so that the air
becomes at once the grave of organic death and the cradle of organic life.
No doubt the ancients suspected this without being able to prove the de
pendence. Euripides seems to have seen it deductively when he describes
the results of decay : —
Then that which springs from earth, to earth returns,
And that which draws its being from the sky
Eises again up to the skyey height
C 2
20 REPORT — 1885.
Tlie consequences of the progressive discoveries have added largely to
our knowledge of life, and have given a marvellous development to the
industrial arts. Combustion and respiration govern a wide range of
processes. The economical use of fuel, the growth of plants, the food of
animals, the processes of husbandry, the maintenance of public health,
the orioin and cure of disease, the production of alcoholic drinks, the
processes of making vinegar and saltpetre — all these and many other
kinds of knowied"e have been brought under the dominion of law. No
doubt animals respired, fuel burned, plants grew, sugar fermented, before
Tve knew how they depended upon air. But as the knowledge was
empirical, it could not be intelligently directed. Now all these processes
are ranched in order under a wise economy of Nature, and can be directed
to the utilities of life ; for it is trup, as Swedenborg says, that ' human
ends always ascend as Nature descends.' There is scarcely a large
industry in the world which has not received a mighty impulse by the
better knowledge of air acquired within a hundred years. If I had time
I could show still more strikingly the industrial advantages which have
followed from Cavendish's discovery of the composition of water. I wish
that I could have done this, because it was Addison who foolishly said,
and Paley who as unwisely approved the remark, ' that mankind required
to know no more about water than the temperature at which it froze and
boiled, and the mode of making steam.'
"When we examine the order of progress in the arts, even before they
are illumined by science, their improvements seem to be the resultants of
three conditions.
1. The substitution of natural forces for brute aiiimal power, as
when Hercules used the waters of the Alpheus to cleanse the Augean
stables; or when a Kamchadal of Eastern Asia, who has been three
years hollowing out a canoe, finds that he can do it in a few hours by
fire.
2. The economy of time, as when a calendering machine produces
the same gloss to miles of calico that an African savage gives to a few
inches by rubbing it with the shell of a snail ; or the economy of produc
tion, as when steel pens, sold when first introduced at one shilling apiece,
are now sold at a penny per dozen ; or when steel rails, lately costing
45Z. per ton, can now be sold at 5/.
3. Methods of utilising waste products, or of endowing them with
properties which render them of increased valae to industry, as when
waste scrap iron and the galls on the oak are converted into ink ; or the
badlysmelling waste of gasworks is transformed into fragrant essences,
brilliant dyes, and fertilising manure ; or when the efl'ete matter of
animals or old bones is changed into lucifcrmatches.
All three results are often combined when a single end is obtained —
at all events, economy of time and production invariably follows when
natural forces substitute brute animal force. In industrial progress the
sweat of the brow is lessened by the conceptions of the brain. How
ADDRESS. 21
exultant is the old Greek poet, Antipater,' when women are relieved of
the drudgery of turning the grindstones for the daily supply of corn.
' Woman ! you who have hitherto had to grind corn, let your arms rest
for the future. It is no longer for you that the birds announce by their
songs the dawn of the morning. Ceres has ordered the loaternymplis to
move the heavy millstones and perform your labour.' Penelope had
twelve slaves to grind corn for her small household. During the most
prosperous time of Athens it was estimated that there were twenty slaves
to each free citizen. Slaves are mere machines, and machines neither
invent nor discover. The bondmen of the Jews, the helots of Sparta,
the captive slaves of Rome, the serfs of Europe, and uneducated labourers
of the present day who are the slaves of ignorance have added nothing
to human progress. But as natural forces substitute and become cheaper
than slave labour, liberty follows advancing civilisation. Machines
require educated superintendence. One shoe factory in Boston by its
machines does the work of thirty thousand shoemakers in Paris who
have still to go through the weary drudgery of mechanical labour. The
steam power of the world, during the last twenty years, has risen from
11^ million to 29 million horsepower, or 152 per cent.
Let me take a single example of how even a petty manufacture improved
by the teachings of science affects the comforts and enlarges the resources
of mankind. When I was a boy, the only way of obtaining a light
was by the tinderbox, with its quadruple materials, flint and steel, burnt
rags or tinder, and a sulphurmatch. If everything went well, if the box
could be found and the air was dry, a light could be obtained in two
minutes ; but xerj often the time occupied was much longer, and the
process became a great trial to the serenity of temper. The consequence
of this was that a fire or a burning lamp was kept alight through the
day. Old Gerard, in his Herbal, tells us how certain fungi were used to
carry fire from one part of the country to the other. The tinderbox
long held its position as a great discovery in the arts. The Pyxidicula
Igniaria of the Romans appears to have been much the same implement
as, though a little ruder than, the flint and steel which Philip the Good
put into the collar of the Golden Fleece in 1429 as a representation of
high knowledge in the progress of the arts. It continued to prevail
till 1833, when phosphorusmatches were introduced ; though I have been
amused to find that there are a few venerable ancients in London who
still stick to the tinderbox, and for whom a few shops keep a small
supply. Phosphorus was no new discovery, for it had been obtained by
an Arabian called Bechel in the eighth century. However, it was for
gotten, and was rediscovered by Brandt, who made it out of very
stinking materials in 1G69. Other discoveries had, however, to be
made before it could be used for lucifermatches. The science of com
bustion was only developed on the discovery of oxygen a century later.
Time had to elapse before chemical analysis showed the kind of bodies
' Analecta Veterum Gracorum, Epig. 39, vol. ii. p. 119.
22 EEroiiT — 1885.
■whicli could be added to phosphorus so as to make it ignite readily. So
it Tvas not till 1833 that matches became a partial success. Intolerably
bad they then were, dangerously inflammable, horribly poisonous to the
makers and injurious to the lungs of the consumers. It required another
discovery by Schrotter in 1845 to change poisonous waxy into innocuous
redbrick phosphorus in order that these defects might be remedied, and
to give us the safetymatch of the present day. Now what have these
successive discoveries in science done for the nation, in this single manu
facture, by an economy of time ? If before 1833 we had made the same
demands for light that we now do, when we daily consume eight matches
per head of the population, the tinderbox could have sujjplied the de
mand under the most favourable conditions by an expenditure of one
quarter of an hour. The lucifermatch supplies a light in fifteen seconds
on each occasion, or in two minutes for the whole day. Putting these
differences into a year, the venerable ancient who still sticks to his
tinderbox would require to spend ninety hours yearly in the production
of light, while the user of lucifermatches spends twelve hours; so that
the latter has an economy of seventyeight hours yearly, or about ten
working days. Measured by cost of production at one shilling and six
pence daily, the economy of time represented in money to our population is
twentysix millions of pounds annually. This is a curious instance of the
manner in which science leads to economy of time and wealth even in a
small manufacture. In larger industries the economy of time and labour
produced by the application of scientific discoveries is beyond all measure
ment. Thus the discovery of latent heat by Black led to the inventions
of Watt ; while that of the mechanical equivalent of heat by Joule has
been the basis of the progressive improvements in the steamengine which
enables power to be obtained by a consumption of fuel less than one
fourth the amount used twenty years ago. It may be that the engines of
Watt and Stephenson will yield in their turn to more economical motors ;
still they have already expanded the wealth, resources, and even the terri
tories of England more than all the battles fought by her soldiers or all
the treaties negotiated by her diplomatists.
The coal which has hitherto been the chief soTirce of power probably re
presents the product of five or six million years during which the sun shone
upon the plants of the Carboniferous Period, and stored up its energy in this
convenient form. But we are using this conserved force wastefuUy and
prodigally ; for, although horsepower in steam engines has so largely in
creased since 1864, two men only now produce what three men did at
that date. It is only three hundred years since we became a manufactur
ing country. According to Professor Dewar, in less than two hundred
years more the coal of this country will be wholly exhausted, and in half
that time will be difficult to procure. Our not very distant descendants
will have to face the problem — What will be the condition of England
without coal ? The answer to that question depends u^dou the intel
lectual development of the nation at that time. The value of the in
ADDEESS. 23
tellcctual factor of production is continually increasing ; wliilc the values
of rav,' material and fuel are lessening factors. It may be that when tlie
dreaded time of exhansted fuel Las arrived, its importation from other
coalfields, such as those of New South Wales, will be so easy and cheap
that the increased technical education of our operatives may largely over
balance the disadvantages of increased cost in fuel. But this supposes
that future Governments in England will have more enlightened views as
to the value of science than past Governments have possessed.
Industrial applications are but the overflowings of science welling
over from the fulness of its measnre. Few would ask now, as was con
stantly done a few years ago, ' What is the use of an abstract discovery
in science ? ' Faraday once answered this question by another, ' What
is the use of a baby ? ' Yet round that baby centre all the hopes and
sentiments of his parents, and even the interests of the State, which
interferes in its upbringing so as to ensure it being a capable citizen.
The piocesses of mind which produce a discovery or an invention are
rarely associated in the same person, for while the discoverer seeks to
explain causes and the relations of phenomena, the inventor aims at pro
ducing new effects, or at least of obtaining them in a novel and efficient
way. In this the inventor may sometimes succeed without much know
ledge of science, though his labours are infinitely more productive when
he understands the causes of the effects which he desires to produce.
A nation in its industrial progress, when the competition of the world
is keen, cannot stand still. Three conditions only are possible for it. It
may go forward, retrogiade, or perish. Its extinction as a great nation
follows its neglect of higher education, for, as described in the proverb of
Solomon, ' They that hate instruction love death.' In sociology, as in
biology, there are three states. The first of balance, when things grow
neither better nor worse ; the second that of elaboration or evolution, as
we see it when animals adapt themselves to their environments ; and the
third, that of degeneration, when they rapidly lose the ground they have
made. For a nation, a state of balance is only possible in the early stage
of its existence, but it is impossible when its environments are constantly
changing.
The possession of the raw materials of industry and the existence of a
surplus population are important factors for the growth of manufactures
in the early history of a nation, but afterwards they are bound up with
another factor — the application of intellect to their development. England
could not be called a manufacturing nation till the Elizabethan age. No
■doubt coal, iron, and wool were in abundance, though, in the reign of
the Plantagenets, they produced little pi'osperity. Wool was sent to
Flanders to be manufactured, for England then stood to Holland as
Australia now does to Yorkshire. The political crimes of Spain from the
reign of Ferdinand and Isabella to that of Philip HI. destroyed it as a
great manufacturing nation, and indirectly led to England taking its
position. Spain, through the activity and science of the Arabian intellect,
24 EBPORT — 1885.
bad acquired many important industries. The Moors and the Moriscoes,
who had been in Spain for a period as long as from the Norman
Conquest of this country to the present date, were banished, and with
them departed the intellect of Spain. Then the invasion of the Low
Countries by Philip II. drove the Flemish manufacturers to England,
while the French persecution of the Huguenots added new manufacturing
experience, and with them came the industries of cotton, wool, and silk.
Cotton mixed with linen and wool became freely used, but it was only from
1738 to the end of the century that the inventions of Wyatt, Arkwright,
Hargreaves, Crompton, and Cartwright started the wonderful modern
development. The raw cotton was imported from India or America, but
that fact as regards cost was a small factor in comparison with the intellect
required to convert it into a utility. Science has in the last hundred
years altered altogether the old conditions of industrial competition. She
has taught the rigid metals to convey and record our thoughts even to
the most distant lands, and, within less limits, to reproduce our speech.
This mai'vellous application of electricity has diminished the cares and
responsibilities of Governments, while it has at the same time altered the
whole practice of commerce. To England steam and electricity have
been of incalculable advantage. The ocean, which once made the coun
try insular and isolated, is now the very lifeblood of England and of
the greater England beyond the seas. As in the human body the blood
bathes all its parts, and through its travelling corpuscles carries force to
all its members, so in the body politic of England and its pelagic exten
sions, steam has become the circulatory and electricity the nervous
system. The colonies, being young countries, value their raw materials as
their chief sources of wealth. "When they become older they will dis
cover it is not in these, but in the cultui'e of scientific intellect, that their
future prosperity depends. Older nations recognise this as the law of
progress more than we do ; or, as Jules Simon tersely puts it — ' That
nation which most educates her people will become the greatest nation,
if not today, certainly tomorrow.' Higher education is the condition of
higher prosperity, and the nation which neglects to develop the intel
lectual factor of production must degenerate, for it cannot stand still.
If we felt compelled to adopt the test of science given by Comte, that its
value must be measured by fecundity, it might be prudent to claim indus
trial inventions as the immediate fruit of the tree of science, though only
fruit which the prolific tree has shed. But the test is untrue in the sense
indicated, or rather the fruit, according to the simile of Bacon, is like the
golden apples which Aphrodite gave to the suitor of Atalanta, who lagged
in her course by stooping to pick them up, and so lost the race. The
true cultivators of the tree of science must seek their own reward by
seeing it flourish, and let others devote their attention to the possible
practical advantages which may result from their labours.
There is, however, one intimate connection between science and in
dustry which I hope will be more intimate as scientific education becomes
ADDRESS. 25
more prevalent in our scliools and universities. Abstract science depends
on the support of men of leisure, either themselves possessing or having
provided for them the means of living without entering into the pursuits
of active industry. The pursuit of science requires a superfluity of wealth
in a community beyond the needs of ordinary life. Such superfluity is
also necessary for art, though a picture or a statue is a saleable commodity,
while an abstract discovery in science has no immediate or, as regards
the discoverer, proximate commercial value. In Greece, when philo
sophical and scientific speculation was at its highest pomt, and when
education was conducted in its own vernacular and not through dead
languages, science, industry, and commerce weie actively prosperous.
Corinth carried on the manufactures of Birmingham and Sheffield, while
Athens combined those of Leeds, Staffordshire, and London, for it had
■woollen manufactures, potteries, gold and silver work, as well as ship
building. Their philosophers were the sons of biarghers, and sometimes
carried on the trades of their fathers. Thales was a travelling oil
merchant, who brought back science as well as oil from Egypt. Solon
and his great descendant Plato, as well as Zeno, were men of commerce.
Socrates was a stonemason ; Thucydides a goldminer ; Aristotle kept a
druggist's shop until Alexander endowed him with the wealth of Asia.
All but Socrates had a superfluity of wealth, and he was supported by
that of others. Now if our universities and schools created that love
of science which a broad education would surely inspire, our men of
riches and leisure who advance the boundaries of scientific knowledge
could not be counted on the fingers as they now are, when we think of
Boyle, Cavendish, Napier, Lyell, Murchison, and Darwin, but would be as
numerous as our statesmen and orators. Statesmen, without a following
of the people who share their views and back their work, would be feeble
indeed. But while England has never lacked leaders in science, they have
too few followers to risk a rapid march. We might create an army to
support our generals in science, as Germany has done, and as France is now
doing, if education in this country would only m.ould itself to the needs
of a scientific age. It is with this feeling that Horace Mann wrote :— ' The
action of the mind is like the action of fire ; one billet of wood will hardly
burn alone, though as dry as the sun and northwest wind can make it,
and though placed in a current of air ; ten such billets will burn well
together, but a hundred will create a heat fifty times as intense as ten —
will make a current of air to fan their own flame, and consume even
greenness itself.'
VI. Abstract Science the Condition for Progress.
The subject of my address has been the relations of science to the public
weal. That is a very old subject to select for the year 1885. I began it
by quoting the words of an illustrious prince, the consort of our Queen,
who addressed us on the same subject from this platform twentysix
years ago. But he was not the first prince who saw how closely science
26 REPORT — 1885.
is bound uj^ with the Avelfare of States. AH, the soninlaw of Mahomet,
the fourth successor to the Caliphate, urged upon his followers that men
of science and their disciples give security to human progress. Ali loved
to say, ' Eminence in science is the highest of honours,' and ' He dies not
who gives life to learning.' In addressing you upon texts such as these,
my purpose was to show how unwise it is for England to lag in the
onward march of science when most other European Powers are using
the resources of their States to promote higher education and to advance
the boundaries of knowledge. English Governments alone fail to grasp
the fact that the competition of the world has become a competition in
intellect. !Much of this indifierence is due to our systems of education.
I have ill fulfilled my purpose if, in claiming for science a larger share in
public education, I have in any way depreciated literature, art, or philo
sophy, for every subject which adds to culture aids in human develop
ment. I only contend that in public education theie should be a free
play to the scientific faculty, so that the youths who possess it should
leain the richness of their possession during the educative process. The
same faculties which make a man great in any walk of life — strong love
of truth, high imagination tempered by judgment, a vivid memory which
can coordinate other facts with those under immediate consideration— all
these are qualities which the poet, the philosopher, the man of literature,
and the man of science equally require and should cultivate through all
parts of their education as well as in their future careers. My contention
is that science should not be practically shut out from the view of a youth
while his education is in progress, for the public weal requires that
a large number of scientific men should belong to the community. This
is necessary because science has impressed its character upon the age in
which we live, and as science is not stationary but progressive, men are re
quired to advance its boundaries, acting as pioneers in the onward march
of States. Human progress is so identified with scientific thought, both
in its conception and realisation, that it seems as if they were alternative
terms in the history of civilisation. In literature, and even in art, a
standard of excellence has been attained which we are content to imitate
because we have been unable to surpass. But there is no such standard
in science. Formerly, when the dark cloud was being dissipated which
had obscured the learning of Gieece and Rome, the diffusion of literature
or the discovery of lost authors had a marked influence on advancing
civilisation. Now, a Chrysoloras might teach Greek in the Italian uni
versities without hastening sensibly the onward march of Italy ; a
Poggio might discover copies of Lucretius and Quintilian without
exercising a tithe of the influence on modern life that an invention by
Stephenson or Wheatstone would produce. Nevertheless, the divorce of
culture and science, which the present state of education in this country
tends to produce, is deeply to be deplored, because a cultured intelligence
adds greatly to the development of the scientific faculty. My argument
is that no amount of learning without science suffices in the present state
ADDRESS. 27
of the world to put us in a position wliicli will enable England to keep
ahead or even on a level with foreign nations as regards knowledge and
its applications to the utilities of life. Take the example of any man of
learning, and see how soon the direct consequences resulting from his
learning disappear in the life of a nation, while the discoveries of a man
of science remain productive amid all the shocks of empire. As 1 am in
Aberdeen I remember that the learned Dutchman Erasmus was intro
duced to England by the encouragement which he received from Hector
Boece, the Principal of King's College in this University. Yet even in
the case of Erasmus — who taught Greek at Cambridge and did so much
for the revival of classical literature as well as in the promotion of spiritual
freedom — how little has civilisation to ascribe to him in comparison with
the discoveries of two other Cambridge men, Newton and Cavendish.
The discoveries of Newton will influence the destinies of mankind to the
end of the world. "When he established the laws by which the motions
of .the great masses of matter in the universe are governed, he con
ferred an incalculable benefit upon the intellectual development of the
human race. No gieat discovery flashes upon the world at once, and
therefore Pope's lines on Newton are only a poetic fancy : —
Nature and Nature'.s laws laj' hid in night,
God said, ' Let Newton be,' and all was liglit.
No doubt the road upon which he travelled had been long in preparation
by other men. The exact observations of Tycho Brahe, coupled with the
discoveries of Copernicus, Kepler, and Galileo, had already broken down
the authority of Aristotle and weakened that of the Church. But though
the conceptions of the universe were thus broadened, mankind had not
yet rid themselves of the idea that the powers of the universe were still
regulated by spirits or special providences. Even Kepler moved the
planets by spirits, and it took some time to knock these celestial steers
men on the head. Descartes, who really did so much by his writings to
force the conclusion that the planetary movements should be dealt with
as an ordinary problem in mechanics, looked upon the universe as a
machine, the wheels of which were kept in motion by the unceasing
exercise of a divine power. Yet such theories were only an attempt to
regulate the universe by celestial intelligences like our own, and by
standards within our reach. It required the discovery of an allpervading
law, universal thioughout all space, to enlarge the thoughts of men, and
one which, while it widened the conceptions of the universe, reduced the
earth and solar system to true dimensions. It is by the investigation of
the finite on all sides that we obtain a higher conception of the infinite —
Willst du ins TJnendliche sclireiten,
Geh nur im Endlichen nach alien Seiten.
Ecclesiastical authority had been already undermined by earnest inquirers
such as Wycliffe and Huss before Luther shook the pillars of the Vatican.
28 REPORT — 1885.
They were removers of abuses, but were confined within the circles of
their own beliefs. Newton's discovery cast men's minds into an entirely
new mould, and levelled many barriers to human progress. This intel
lectual result was vastly more important than the practical advantages
of the discovery. It is true that navigation and commei'ce mightily
benefited by oui better knowledge of the motions of the heavenly bodies.
Still, these benefits to humanity are incomparably less in the history of
progress than the expansion of the human intellect which followed the
withdrawal of the cramps that confined it. Truth was now able to
discard authority, and marched forward without hindrance. Before this
point was reached Brnno had been burned, Gralileo had abjured, and both
Copernicus and Descartes had kept back their writings for fear of offend
ing the Church.
The recent acceptance of evolution in biology has had a like effect in
producing a far profounder intellectual change in human thought than
any mere impulse of industrial development. Already its application to
sociology and education is recognised, but that is of less import to human
progress than the broadening of our views of Nature.
Abstract discovery in science is then the true foundation upon which
the superstructure of modern civilisation is built ; and the man who
would take part in it should study science, and, if he can, advance it for
its own sake and not for its applications. Ignorance may walk in the path
lighted by advancing knowledge, but she is unable to follow when science
passes her; for, like the foolish virgin, she has no oil in her lamp.
An established truth in science is like the constitution of an atom in
matter — something so fixed in the order of things that it has become
independent of further dangers in the struggle for existence. The sum
of such truths forms the intellectual tieasure which descends to each
generation in hereditary succession. Though the discoverer of a new
truth is a benefactor to humanity, he can give little to futurity in com
parison with the wealth of knowledge which he inherited from the past.
We, in our generation, should appreciate and use our great possessions —
For me jour tributary stores combine,
Creation's heir ; the world, the world is mine.
EEPOETS
ox THE
STATE OF SCIENCE.
EEPORTS
ON THE
STATE OF SCIENCE.
Report of the Committee, consisting of Professor G. Carey Foster,
Sir W. Thomson, Professor Ayrtox, Professor J. Perry, Pro
fessor W. Gr. Adams, Lord Kayleigh, Dr. 0, J. Lodge, Dr. John
HoPKiNSON, Dr, A. ]Muirhead, ]Mr. W. H. Preece, Mr. H. Taylor,
Professor Everett, Professor Schuster, Dr. J. A. Fleming, Pro
fessor Gr. F. Fitzgerald, ]Mr. R. T. Gla/ebrook {Secretary), Pro
fessor Chrystal, ]Mr. H. Tomlixson, and Professor W. Garnett,
appointed for the pmrpose of constructing and issuing practical
Standards for use in Electrical Measurements.
The Committee report tliat during the year the standards of resistance,
ia terms of the legal ohm referred to in the last Report, have been con
structed, and their values determined ia accordance with the resolution
adopted on June 25, 1884.
The oneohm standards were generally referred to the original B.A.
units of the Association by combining in multiple arc with the standard
one of the 100 B.A. units, and determining by Carey Foster's method the
difference between the combination and a B.A. unit, and then assuming',
in accordance with the resolution, that 1 B.A. unit ^ '9889 legal ohm.
The following values were thus found for the two standards.
The temperatures were taken by a thermometer graduated to tenths
of a degree centigrade, which had been compared with the Kew standards.
Resistance Coil, Elliott, No. 139, ^ 100.
Date
Temperature
Resistance
Nov. 24, 1884
,. 26, „
,, 27, „
.. 28, „
Dec. 5, „
12
July 30,' 188.5
,. 28, „
ll°4
11°G
12°9
13°5
13°5
15°3
n°2
18°^l
•99878
•99890
•99916
•99930
•99931
•99979
1^00027
1OOOGl
Mean value .
Temperature cosfEcient
■999515, at 14°^1 C.
•000271
32
EEPORT — 1885.
Resistance Coil, Elliott, No. 140, ^ 101.
Date
Temperature
Resistance
Nov. 24, 1884 .
ll°4
•99813
,. 25, „
ll°5
99815
Dec. 2, „
12°8
•99847
Nov. 27, „
12°9
•99851
Dec. 5, „
18°4
•99865
„ 12, „
15°4
•99917
July .30, 1885
17°2
99961
„ 29. „
18=0
•99983
Mean value .
Temperature coefficient
•998815, at 14°1 C.
•000259
The tenolim standards were tlien compared with the oneohm by
means of the arrangement suggested by Lord Rayleigh, and described in
the Report for 1883, and from these values were obtained for tlie coils of
higher resistance.
The results are contained below.
No. of Coil
Resistance
Temperature
No. 141, ;^ No. 102
1000103
lG°7
No. 142, ;^ No. 103
1000169
16°75
No. 143, ;^No. 104
999977
16°05
No. 144, "^ No. 105
1000108
16°05
No. 145, "^ No. 106
1,000306
17°4
No. 146, ;^ No. 107
1,000276
17°4
No. 147, ^ No. 108
10,0024
17°35
No. 148, ^ No. 109
10,0024
17°35
These experiments were carried out at the Cavendish Laboratory by
the Secretary and Mr. H. Wilsou, of St. John's College.
At the request of M. Mascart, the Secretary compared with the
legal ohms of the Association three mercury copies of a legal ohm,
constructed by M. J. R. Benolt, of Paris. A detailed account of these
experiments was laid before the Physical Society.' The values found are
given below.
No. of Tubes
Value found bv
M. J. R. Bcnoit
Value found bv
K. T. G.
Diff
37
38
39
100045
100066
•99954
99990
100011
99917
•00055
■00055
■00037
Moan
100022
•99972
•00049
' ridl. Mil//. Oct. 1885.
ON STANDARDS FOR USE IN ELECTRICAL MEASURE5i'ENTS.
33
The work of testing resistancecoils has been continued, and a table
of the values found for the various coils examined is given.
British Association Units.
No. of Coil
Eesistance in B.A. Units
Temperature
Elliott, No. 122 f
$^ No. 61 1
Elliott, No. 58
100163
100017
99885
99834
19°8
15°2
10' 5
14°05
Legal Ohms.
No. of Coil
Jlesistance in Legal Ohms
Temperature
"^ No. 150
^ No. 151
Elliott, 149, '^ No. 152
Elliott, 136, '^ No. 153
:^ No. 154
•99895
•99974
•99912
•99977
100032
ll°7
13°9
12°5
12°4
17°3
The Committee hope that arrangements may be made for issuing
standards of electromotive force and constructing standards of capacit3\
In conclusion, they would ask to be reappointed, with the addition of the
names of Professor J. J. Thomson and Mr. W. N. Shaw, with the re
newal of the unexpended grant of 60/.
Report of the Committee, consisting of Professors A. Johnson
(Secretary), J. Gr. MacGtREGOR, J. B. Cherriman, H. T. Bovey,
and Mr. C. Carpmael, appointed for the purpose of promoting
Tidal Observations in Canada.
The Committee have represented to the Canadian Government the
importance of publishing tidetables for Canadian waters, and the neces
sity for this purpose of establishing stations for continuous tidal observa
tions, recommending that the observations be subsequently reduced by
the methods of the British Association.
They have pointed to the example of the United States Government,
which has provided tidetables for both the Atlantic and Pacific coasts.
In urging the practical side of the question they have more especially
referred to the tidetables for British and Irish ports published by the
Admiralty, which give the rate and set of the tidal currents in the waters
surrounding the British islands ; and they have drawn attention to the
heavy annual losses caused by ignorance of these currents in Canadian
waters, as shown by the wreck list.
1885. D
34 EEPORT — 1885.
In ordei' to strengthen their representation from this point of view,
they deemed it well to get the opinions of Boards of Trade and ship
owners and shipmasters. On inquiry it appeared that the Montreal
Board of Trade were at the very time considering the qnestion, which
had been brought independently before them. On learning the object of
the Committee they gave it their most hearty support, and addressed a
strong memorial on the subject to the Dominion Government.
The Boards of Trade of the other chief ports of the Dominion also
sent similar memorials. The shipowners and masters of ships, to whom
application was made, were practically nnanimons in their testimony as
to the pressing need for knowledge on the subject.
The representations of your Committee were made through the
Minister of Marine, with whom an interview was obtained, at which a
memorial was submitted. Copies of the answers of the shipmasters (a
large number of which had been received) were submitted at the same
time. Full explanations, in reply to the inquiries of the Minister, were
given, more especially on practical points connected with the proposed
observations at fixed stations and the reductions, for which your Com
mittee are largely indebted to a corresponding committee appointed by
the Council, consisting of the Right Hon. Sir Lyon Playfair, Professor J.
Couch Adams, Sir William Thomson, and Professor Darwin.
During the session of Parliament the Royal Society of Canada also
addressed petitions to the GovernorGeneral and the two Houses of
Parliament, strongly urging the need of tidal observations.
The reply of the Minister of Marine stated that, owing to the large
outlay on the Georgian Bay Survey, and on the expedition to Hudson's
Bay during the past summer (18S5), the Government did not propose to
take action in the matter of tidal observations at present. This un
favourable answer, it will be observed, is made to depend on a temporary
financial condition, and your Committee have reason to believe that if
the financial ]irospects improve by next session of Pailiament, the Govern
ment will take the matter into earnest consideration ; they therefore
suggest that the Committee be reappointed.
Fifth Report of the Committee, consisting of j\Ir. John jNIurray
(Secretary), Professor Schuster, Professor Sir William Thomsox,
Professor Sir H. E. KoscoE, Professor A. S. Herschel, Captain
W. DE W. Abxey, Professor Bonney, Mr. E. H. Scott, and Dr. J.
H. Gladstone, appointed for the purpose of investigating the
practicability of collecting and identifying Meteoric Dust, and
of considering the question of undertaking regular observations
in various localities.
The Secretary reported that collecting apparatus had been sent to various
oceanic islands, and that a report would be prepared by next year on the
specimens received.
ON THE HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 35
Third Report of the Gommittee, connsting of Professors G. H.
Darwin and J. C. Adams, for the Harmonic Analysis of Tidal
Observations. Drawn up by Professor G. H. Darwin.
I. Record of Work during the past Year.
The edition of the compntafcion forms referred to in the second report is
now completed, and copies ai'e on sale with the Cambridge Scientific
Instrument Company, St. Tibbs' Row, Cambridge, at the price of 2s. GtZ.
each. Some copies of the first report, in which the theory and use of
those forms are explained, are also on sale at the same price. A few
copies of the computation forms have been sent to the librarians of some
of the principal Scientific Academies of Europe and America.*
In South Africa, Mr. Gill, at the Cape, and Mr. Neison, at Natal, are
now engaged in reducing observations with forms supplied from this
edition.
A memorial has been addressed to the Government of the Dominion of
Canada, urging the desirability of systematic tidal observation, and the
publication of tidetables for the Canadian coasts. There seems to be
good hope that a number of tidegauges will shortly be set up on the
Atlantic and Pacific coasts, and in the Gulf of the St. Lawrence. The
observations will probably be reduced according to the methods of the
British Association, and the predictions made with the instrument of the
Indian Government.
Major Baird has completed the reduction of all the tidal results obtained
at the Indian stations to the standard form proposed in the Report of 1883,
and Mr. Roberts has similarly reduced a few results read before the
Association by Sir William Thomson and Captain Evans in 1878. All
these are now being published in the ' Proceedings of the Royal Society,'
in a jmper by Major Baird and myself.
A large number of tidal results have been obtained by the United States
Coast Survey, and reduced under the superintendence of Professor Ferrel.
Although the method pursued by him has been slightly different from that
of the British Association, it appears that the American results should be
comparable with those at the Indian and European ports. Professor
Ferrel has given an assurance that this is the case ; nevertheless, there
appears to be strong internal evidence that, at some of the ports, some
of the phases should be altered by 180°. The doubt thus raised will
probably be removed, and the paper before the Royal Society will
afford a table of reference for all — or nearly all — the results of the
harmonic method up to the date of its publication.
The manual of tidal observation promised by Major Baird is now com
pleted, and will be published shortly. This work will explain fully all
the practical difficulties likely to be encountered in the choice of a station
for a tidegauge, and in the erection and working of the instrument.
Major Baird's great experience in India, and the success with which the
operations of which he has had charge have been carried out, render his
' Namely, the Koyal Societies of London and Edinburgh, the Royal Irish Aca
demy, the Academies of Paris, Berlin, and Vienna, the United Coast Survey, and the
Cambridge Philosophical Society.
D2
36 REPOKT — 1885.
advice of great value for tlie prosecution of tidal observation in other
conntries. The work also explains the method of measuring the tide
diaorams, entering the figures in the computation forms, and the sub
sequent numerical operations.
II. Certain Factors and Angles used in the Reduction of Tidal
Observations.
In completing the reduction of the results of harmonic analysis to the
standard form, a number of angles and factors are required which de
pend on the longitude of the moon's node. Tables of these angles and
factors have been computed under the superintendence of Major Baird.'
It may happen, however, that the tables are inaccessible to the computer,
and the computation from the full formulae might be somewhat laborious.
It happens that the angles r, £, v', 2v" (the meanings of which are ex
plained in the Report of 1883) are all expressible in the form
A sin iV+B sin 2iV+C sin 3i^+ ,
where N is the longitude of the moon's node, and that the coefiBcients
diminish with such rapidity that the first two terms are probably sufficient
for all practical purposes.
Also the several factors f are reducible to the form
A + B cos N+G cos 2^+ . . . . ,
and three terms are practically sufficient.
I have obtained the approximate formulze given below in this form.
The rigorous results having been tabulated, it appeared easier to work
from them instead of from analytical expressions in terms of the longitude
o£ the moon's node. I find, then, the following results : —
Schedule I. Approximate Formula; for Angles.
.' =12°9 sin A^l°3 sin 2N,
I =,'l°07 sin N,
(forK,) v' =z8°8sinN0°6sm2N,
(for Ka) 2»'"=17°8 sin N 0°5 sin 2^^,
Also A =16°51 + 3°44 cos ^0°19 cos 2N, and A,=16°36.
For the meanings of A and A^ the reader must refer to Part IV.
Approximate Formulce for Factors f.
For Mj and other tides,
f = — cos^ U ^10003 _ 0373 cos iVl0002 cos 2N.
cos'' ^o) cos* ^i
For 0, f= . ^'" ^,^"^' ^^^ , =10088 + 1886 cos J^0146 cos 2A^.
sm w cos'^ io) cos* ^i
ForK2 f= 10243 + 2847 cos A'+ 0080 cos 2Jv^.
ForKi f=l0060 + 1156 cos Jv^ 0088 cos 2iVr.
ForMf . . f= . /'''' ^, , =10429 + 4135 cos .^•0040 cos 2^.
sm'' <i> cos* ^4
• Some of these are given in the Report of 1883.
ON THE HARMONIC ANALTSIS OF TIDAL OBSERVATIONS. 37
For Mm,
(1— Isin^w) (1— fsin^i)
f= ^7~K^]f \ ■ ., .. =l0000r299 cos N+ 0013 cos 2N.
Even if all the terms in 2N were omitted, the approximations might be
good enough for all practical purjioses.
III. On the Periods chosen for Harmonic Analysis in the
Computation Forms.
Before proceeding to the subject of this section, it may be remarked
that it is unfortunate that the days of the year in the computation forms
should have been numbered from unity upwards, instead of from zero, as
in the case of the hours. It would have been preferable that the first
entry should have been numbered Day 0, Hour 0, instead of Day 1,
Hour 0. This may be rectified with advantage if ever a new issue of the
forms is required, but the existing notation is adhered to in this section.
The computation form for each tide consists of pages for entry of the
hourly tideheights, in which the entries are grouped according to rules
appropriate to that tide. The forms terminate with a broken number of
hours. This, as we shall now show, is erroneous, although this error may
not be of much practical importance.
In § 9 of the Report for 1883 the following passage occurs : —
' The elimination of the effects of the other tides may be improved by
choosing the period for analysis not exactly equal to one year. For
suppose that the expression for the height of water is
Ai cos ?!i< + Bi sin jii^ + Ao cos 7i2ifB2 sin «2^ • • • (^1)
* where 11.2 is nearly equal to «i, and that we wish to eliminate the
n2tide, so as to be left only with the «itide.
' Now, tbis expression is equal to
{A,+A2Coa (?ii— ?i2)«^ — Bo sin («i — «2)^} cos n^t)
+ [Bi+A2 sin (71,— «2)i + B2 COS ('h— 7J2)0 sin «ii] *
' That is to say, we may regard the tide as oscillating with a speed tiy,
but with slowly varying range.'
Although this is thus far correct, yet the subsequent justification of
the plan according to which the computation forms have been compiled
is wrong.
In the column appertaining to any hour in the form we have n^t a
multiple of 15°, if n^ be a diurnal, and of 30°, if 71^ be a semidiurnal
tide.
Consider the column headed 'phours ' ; then nit=15° p for diurnals,
and 30°_p for semidiurnals.
Hence (62), quoted above, shows us that, for diurnal tides, the sum of
all the entries (of which suppose there ai'e 2) in the column numbered
yhours, is
38 EEPORT — 1885.
cos lb°p{A^q + AJcoa(',Hn.^^ + co3[(in,7io)(^^^ + ^J]
+ cos[0h«2)('2^ + i^')]+ . . ."]+P,[&c.]}+sml5°p{&c.} (a)
And for semidiurnal tides the arguments of all the ciicnlar functions in
(a) are to be doubled.
Now, we want to choose such a number of terms that the series by
which A2 and Bo are multiplied may vanish. This is the case if the series
is exactly reentrant, and is nearly the case if nearly reentrant.
The condition is exactly satisfied for diurnal tides, if
{ni—7i2)q — =27rr,
where r is either a positive or negative integer. And for semidiurnal
tides, if
(?i, — ^2)2 — =27n'.
That is to say,
(^^ni—n2)q—nir, for diurnal tides,
or
(h, — H2)2=5'^i'*> for semidiurnal tides.
It is not worth while attempting to eliminate the effect of the semi
diurnal tides on the diurnal tides, and vice versa, because we cannot be
more than a fraction of a day out, and on account of the incommensurability
of the speeds we cannot help being wrong to that amount.
S Series.
Now suppose we are analysing for the Sj tide, and wish to minimise
the effect of the M2 tide.
Then n,=2(y— »?)=2 xl5° per hour,
712 = 2(70),
9;i?!2=2(<r'?)=l°0]58958 per hour.
The equation is
l°01589582=15°r.
If r=25, 2=36913.
Thus 25 periods of 2((7 — ??) is 36913 mean solar days. It follows,
therefore, that we must sum the series over 369 days in order to be as
near right as possible.
Now this is equally true of all the columns, and each should have 369
entries.
Hence, in order to have 369 entries in each column, the present 83
computation form should have the last three entries cut off. The divisors
are to be, of course, changed accordingly.
M Series.
Now consider that we are analysing for Mg, and wish to minimise the
effect of the S., tide. Hence
ON THE HARMONIC ANALYSIS OF TIDAL OBSEEYATIONS. 39
n,=2(7 ,t)=2 X 14°4920521 per hour,
n2 = 2(yr,),
«,,i2=_l°0158958 per Lour.
Hence, taking r negative, the equation is
l°01589582=14°4920521r.
If 525, 2=35663.
Thus 25 periods of 2(r7 — rj) is 356'63 of mean lunar time.
It follows, therefore, that we must have 857 entries in each column.
Thus the M, computation forni should have the row numbered 357
complete, adding 9 more entries.
There are no ' changes ' amongst these 9 entries. The divisors are
to be modified accordingly, here and in all subsequent cases.
K Series.
To minimise the effect of Mg on K,, we have
ni = 2y=2 xl5°041068G per hour,
«2 = 2(y0,
ni«2=2(T,,) = l°0158958 per hour.
l°0158958g=15°0410C86r.
If r=25, 2=37014.
Hence we should complete the row numbered 370.
The last 3 entries of the existing tables are to be cut off.
To minimise the effect of O on K,, we have
w, = y=15°0410686 per hour,
112=7 2<r,
w,H2=2<T=l°0980330 per honr.
l°09803302=15°0410686r.
If r=27, 2=36985.
Thus 2=370 again gives the best result, and confirms the conclusion
from the above.
The N Series.
Here 7ii=2y3<7 + ir=2 xl4°2198648 per hour.
To minimise the effect of M2,
«2=2y — 2(r,
ni— ??2=(<T'57)=0°5443747 per hour,
054437472=14°2198648r.
If r=13, 2=33958.
Hence we should complete the row numbered 340.
There is no justification for the alternative offered in the computation
forms of continuing the entries up to 369'' 3'^ of mean solar time.
The L Series.
Here ni = 2y(T ^=2 xl4°7642394 per hour.
40 REroKT — 1885.
To minimise tlie effect of M2,
)i,2^2y — 2(T,
«j —n.2 = (T — '!!r=0°'5i4>S74i7 per hour.
0'54437472=14°7642394r.
If, .=13, f^=35258.
Hence we should complete the row numbered 353.
There is no justification for the alternative offered in the computa
tion forms of continuing the entries up to 369*^ 3*^ of mean solar time.
The r Series.
Hero 92,=273a'sr + 2;j=2 xl4°2562915 per hoar.
To minimise the effect of M.,,
^!2 = 27 — 2(7,
n
i/2=ow+2>j=0°4715211 per hour.
1 —"2
0471o211';=14256291.5).
Ifr=ll, 2=3326,
Hence we should complete the row numbered 333.
There is no justification for the alternative offered in the computation
forms of continuinp: the cnti ies up to 369'' 3^ of mean solar time.
The X Series.
Here ni=27a + 'z^2;/ = 2 xl4°7278127 per hour.
To minimise the effect of Mj,
n,=2y2(T,
«,,— 772=(T + «r — 2>;=0°4715211 per hour.
0471521l2=147278127r.
If r = ll, 2=34358.
Hence we should complete the row numbered 344.
There is no justification for the alternative offered in the computation
forms of continuing the entries up to 369*^ 3*^ of mean solar time.
The 2N Series.
Here w,=2y4ff + 2'ar=2 xl3°9476774 per hour.
To minimise the effect of Mj,
^2=27 — 2t,
nin2=2(o'nT)=l°0887494 per hour.
l08874942=139476774).
Ifr=26, 2=33308.
Hence we must complete the row numbered 333.
The T Series.
Here 7ii=273»;=2 xl4°9794657 per hour.
To minimise the effect of M2,
n^=2y2rr,
ni«2=2T3T = 0°9748272 per hour.
097482722=149794657r.
Ifr=24, 3=36879.
ON THE HAiniONIC ANALYSIS OF TIDAL OBSERVATIONS. 41
Hence we must complete the row numbered 369.
The'R Series.
Here wi=2y»;=2 x 15°0205343 per hour.
To minimise the effect of Mj,
no=2r2a,
71, — «2=2ff — ii=l°"0569644 per hour.
l0569644(7=150205343).
If r=25, 2=35528, and r=2G, g=36949.
Hence we should either complete the row numbered 355 or that
numbered 369.
The 2MS Series.
Here ni = 2y4(T + 2»;=2 xl3°9841042 per hour.
To minimise the effect of M2,
«2=2y2^,
M, 7i2= 2(<T7;) = 1°0158958 per hour.
l'0158958r/=139841042r.
If r=24, 2=33037, and ?=25, 2=04413.
Hence we should either complete the row numbered 330 or that
numbered 344.
The 2SM Series.
Here Wi=2y + 2(r4rj=2 xl5°5079479 per hour.
To minimise the effect of M,,
«2=2y2^,
«,n2=4(ff— r?)=2°0317916 per hour.
203179162=155079479).
If r=48, 2=36637.
Hence we should complete the row numbered 366.
The Series.
Hero . n,=y2(r=13°9430356 per hour.
To minimise the effect of Kj,
nin2=2ff=l°0980330 per hour.
l09803302=139430356>.
If r=27, 2=34285.
Hence we should complete the row numbered 343, cutting off the
last three entries in the present forms.
The P Series.
Here «i=y2,,=14°9589314 per hour.
It is open to question whether it is best to minimise the effect of
K, or of O.
42 EEroRT — 1885.
For Ki take '>H=y,
,ij,i2=2»j=0°0821372 per hour.
00821372<7=149589314r.
Ifr=2, 2=36424.
Hence we should complete the row numbered 364.
For O, take ^2=7 — 2(t,
,;.,_7i2=^2((T— 7j)=l°'0158958 per hour.
l01589582=149589314r.
Ifr=25, 2=36812.
Hence we should complete the row numbered 368.
It is better to abide by this, for in the former case n^ —n^ varies very
slowly ; and we may be satisfied that on stopping with row 368 the effects
of and Kj will both be adequately eliminated.
The J Series.
Here 7ii = y + (r— 'ct=15°5854433 per hour.
To minimise the effect of Kj,
«2=r,
Wj— n2='7 — 'nr=0°'5443747 per hour.
05443747(7=155854433*.
If r=12, 2=34356, and r=13, 2 = 37219.
To minimise the effect of O,
Wo=:y — 2(r,
«j— n2=3(Tc7=l°6424077 per hour.
l64240772=155854433r.
If r=36, 2=3416, and r=39, 2=37009.
Since in the latter case n^ — Ur^ varies three times as fast as in the
former, it will be better to abide by this, and stop either with the row
numbered 342 or that numbered 370.
The Q Series.
Here «i=y3(r + '=7=13°3986609 per hour.
To minimise the effect of K,,
?i2=y,
,ii_,j2=(3aw) = l°6424077 per hour.
l64240772=133986609r.
If r =38, 2 = 31000.
To minimise the effect of O,
7i2=y — 2(T,
n, — n2= — (ff — 'nr) = — 0°5443747 per hour.
054437472=133986609r.
If r=12, 2=30736.
Since in the former case ni—V2 varies about three times as fast as in
ON THE HAKMONIC ANALYSIS OF TIDAL OBSERVATIONS.
43
the latter, it will be better to abide by the former, and stop with the row
numbered 310.
With regard to the quaterdiurnal and terdiurnal tides, it does not
signify where we stop ; but it seems more reasonable to stop with the
exact year of 365 mean solar days. These tides are called MS, MN,
MK, 2MK.
Schedule II.
Periods over which the Harmonic Analysis should extend.
Initial of series
Number of day and hour of
last entry in special time
Period elapsino; from O"* of spe
cial day 1 to 23'' of last special
day in mean solar hours
s
3691 23^
368'' 23h
M
357 23
369 11
K
370 23
368 23
N
340 23
358 15
L
353 23
358 14
V
333 23
350 8
X
344 23
350 8
2N
333 23
358 2
T
369 23
369 11
E
355 23
or 370 23
354 11
or 369 11
2MS
330 23
or 344 23
353 22
or 368 23
2SM
366 23
353 23
343 23
368 23
P
368 23
368 23
J
342 23
or 370 23
329 3
or o56 1
Q
310 23
347
In the second column the numbers are given to the nearest mean
solar hour.
44
EEroET — 1885.
IV. A Comparison of the Haemonic Treatment of Tidal Observations
WITH THE Older Methods.
§ 1. On the Mefliod of Computing Tidetables.
There is nothing in the harmonic reduction of tidal observations
which necessitates recourse to mechanical prediction of the tides. It
may happen that it is desirable to produce a tidetable by arithmetical
processes, and that the computers prefer to use the older methods of
corrections, or it may be desired to obtain the tidal constants in the har
monic notation from older observations. For either of these purposes it
is necessary to show how the liarmonically expressed results may be
converted into the older form, so that the constants for the fortnightly
inequality in time and height, and the corrections for parallax and
declination, may be obtained from those of the harmonic analysis, and
conversely.
In the following sections I propose, therefore, first to reduce the har
monic presentment of the resultant tide into the synthetic form, where
we have a single harmonic term depending on the local mean solar time
of moon's transit, and on corrections depending on the R.A., declination,
and parallax of the perturbing bodies. Subsequently it will be shown
how a synthesis may bo carried out more simply by retaining the mean
longitudes and elements of the orbits.
§ 2. Notation for Mean Heights and llefardations derived from the Harmonic
Method.
The notation of the Report of 1883 is adopted ; and I shall carry the
approximation to about the same degree as has been adopted by the older
writers. Closer approximation ma}', of course, be easily obtained.
In the Report of 1883 the mean height ' of a tide is denoted by H,
and the retardation or lag by k. In the present note it will be necessary
to refer to several of the H's and /.'s at the same time, and therefore it
is expedient to introduce the following notation : —
Schedule III.
Initial of
Mean height
Retardation
Initial of
Mean height
Retardation
tide
(H)
(«)
tide
(H)
i'^)
Ma
M
2/x
L
L
2\
S2
S
2i:
T
T
2C
Lunar K,
K"
2/v
R
B
24
Solar K2
K!'
2/.
M'
/'
K,
K2
2^
P
S'
<:'
N
N
2r
1
K,
^1
'"i
In this schedule we assume T and R (of speeds 2y — 3ij and 27 — 77) to
have the same lag as S2 ; and we use v in a new sense, the old )■, the
' I use height to denote semirange. All references to this Report will simply
be by the date 1883.
ON THE HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 45
R.A. of the intersection of the equator with the lanar orbit, being
denoted by r^. The initials of each tide are used to denote its height at
any time.
§ 3. Introduction of Sourangles, Parallaxes, and Declinations.
We must now get rid of the elements of the orbit and of the mean
longitudes, and introduce hourangles, declinations, and parallaxes.
At the time t let a, ^, xp he 5 'sR.A., and declination, and hourangle,
and n^, ^'^, \p^, © 's R.A., and declination, and hourangle.
Let Z be 5 's longitude in her orbit measured from ' the intersection,'
and a — I'o (I'o being the r of 1883) be D 's R.A. measured from the
intersection.
The annexed figure exhibits the relation of the several angles to one
another.
The spherical triangle affords the relations
tan (fi — ro)^cos/tanZ, sin o=sin7sinZ .... (1)
From the first of (1) we have, approximately,
a = ?+r^tan2iIsin2Z (2)
Now, s — s is the moon's mean longitude measured from J, and s—p is
the mean anomaly. Hence, approximately,
Z = s— ^2e sin(s— ;)) (3)
And therefore, approximately,
a = s + »'o — s + 2esin(s— J)) — tan^^/sin 2(s— ^) . . . (J.)
Now, t\li being the sidereal hourangle,
4. = <7ia (5)
Therefore, from (4) and (5),
f + /i_s(r„£)=i//f2esin(sp)tan2iZ"sin2(s£). . (6)
By the second of (1) we have, approximately,
cos2c = l — sinl4Jsin2/cos2(s— I) .... (7)
Hence, if A be such a declination that cosA is the mean value of cos^ o,
we have
cos^A =1— isin^ J )
(8)
^2a,
and cos^A^= 1 — ^sin^
From this we have (neglecting terms in sin'* A) the following relations: —
cos^ ^1= cos^A, sinlcos^ il= V2sinAcosA, sin^ J= 2sin2 A,
cos'* 1^ = cos' A ^, sinwcos^^w^ %/2sina) cos w, sinw=2sin2 A^.
46
REPOET 1885.
Thus we may put
cos* il
cos^ A
sin2A\
sin Jcos^ jl
sin (o cos^ ^ w CDS'* it sin 2 A^
tanHI=itan2A
cos* ^a> COS* ^i COS A,
sin^I _sin2A
sin2w(l — osin^t) sin'^A/
An approximate formula for A and the ralue of A, are
A = 16°51 + 3°44cosN0°19 cos 2N, A =16°36
The introduction of A and A^ in place of I and w entails a loss of
accuracy, and it is only here made because former writers have followed
that plan. It may easily be dispensed with.
Now let us write
(?)
(10)
D=cos2(s— i),
n=cos(s— p),
From (7) and (8),
J. cos^ c — cos^ A
sm^ A
D'=sin2(s£)'
n'=sin (s— p)
J, sine cos? do
ffsin^A dt
(11)
(12)
Then, if we write for the ratio of the moon's parallax to her mean paral
lax P, we have
P — 1 = ccos(s— j>),
and
n'=
dP
(13)
n = (Pl),  , . n
e e{rT — ij) at
Hence D, D', IT, IT are functions of declinations and parallaxes. The
similar symbols with subscript accents are to apply to the sun.
Now (G) may be written by aid of (9) and (11),
o[; + 7,_5_(,,^_t)]=2J/ + 4en'D'tan2A . . . (14)
The lefthand side of (14) is the argument of M, (see Sched. B. i.
1883), and from (9) the factor of M., is cos^A/cos^A,. Hence, subtracting
the retardation 2ju from (14) we have
(Mo)=^^3/cos[(2^H4en'D'tan2A)2/x],
' cosA;
expanding approximately,
(Mo)=^^4^3fcos2(>i.A.)
cos^'A^
cosA
cos"^A,
sin^A
cos^A,
n'43fesin2(4//i)
D'3Isin2(J.^) (ir.)
We shall see later that the two latter terms of (15) are nearly
annulled by terms arising from other tides, and as in the case of the sun
the rates of change of parallax and declination are small, we may write
by symmetry,
^ (So) = Scos2(v/.,0 (IG)
ON THE HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 47
In all the smaller tides we may write
A general formula of transformation will be required below. Thus, if
cos2a'^X, sin2.ii=X',
:^ sin2(;/.^) . (17)
C0S2(ct — yti) yr r/ V y
The lunar Kn tide.
From Sched. B. i., 1883, we have
Lunar K2=^,^'°!^Ji:"cos2r^ + 7iro'^]
sin(.i(l— l^sin^t) o J
''"^Z"cos2[v;/+(s0'^]
sm
Applying (17) with X=D, X'=D', a=/., and taking the lower sign,
In the case of the sun we neglect the terms in D', for the same reasons
as were assigned for the similar neglect in (16), and have
Solar Ko=7r/'Z),cos2(4.,/.) (19)
The tide N.
From Schedule B. i.. Report 1883,
COS'^WCOS'^l ^ V z/ J
^^'^ (N)=^^^cos2[;^,.K«p)].
Then applying (17) with X=U, X'=n', a = r, and taking the upper
sign, bat writing ^t — r instead of j' — ^(, because this tide being slower
than M2 suffers less retardation,
(N)=^5^^r(n+tan2(^r)n')cos2(;//r)
The tide L.
We shall here omit the small tide of speed 2y — ff + 'nr, by which the
true elliptic tide is perturbed. Thus the B in the column of arguments
in Sched. B. i., 1883, is neglected, and we have
48 KEPOKT — 1885.
Applying (17) with X=n, X'=n', n=\, and taking the lower sign,
and changing the Bign of the whole, because of the initial negative sign,
(L) = ^^^^Lr(ntan2(\//)n')cos2(v/.X)
COS^!k/ L
n2(+rtj . (21)
4
I
cos2(\— y^t)
The sum o/N and L.
In order to fuse these terms an approximation will be adopted. The
L tide is just as much faster than Mo as N is slower, but the N tideshould
be nearly 7 times as great as the L tide; hence the tan2(\/t) in (21)
will be put equal to tan2(^)0. We then have
(N) + (L)=^r(n + tan2(/.On')(^cos2(»/.,')Lcos2(;/.\)) J
COS ^/L "
+ n'(A"sec2(/x.) + Lsec2(\^))sin2(^^.)]
J^cos2rJ/>0— Lcos2(>/.X)=cos2;/.(A^cos2)'Lcos2\)
+ sin 2ijt'(W'sin 2iisin2X).
Then writing
, o iV'sin2i' — Lsin2\ /^qx
JVcos2>'— Lcos2a
BO that £ is nearly equal to r, we have
^ ^^^ ■' cos^A^ cos2£ L J
+ £!^r(i^sec2(^<.')+i>8ec2(\/z))sin2(>^^)] . (23)
cos'AX J
In the symmetrical term for the sun, with approximation as in (16), j
^^^^^ (T) + (R)=(rii;)n,cos2(;//0 (24)
This terminates the semidiurnal tides which we are considering; but 
before proceeding to collect the results some further transformations must
be exhibited. r^, , • n n /i tx
Let us consider the function D + xB', where x is small. From (12)
we see that n • ^ 5 js
cns'c— cos'^A 1 2 sine cos cad
^ sin^A (T sin'A at
Hence, if S' be the moon's declination at a time earlier than the time of
observation by x/2cr, then
^_^^^,^cosVcos^_ .
sm'^A
Hence, in (17),
■n . ^ or ^n' cos^o'— cos^A .^..
Dftan2(K — w)!* = r:7\ .... (.^0;
' sm^A
when h' is the moon's declination at time tV^57°3 tan 2(k^)/2(7. The
period 57°3 tan2((c;:x)/2<7 may be called ' the age of the declinational
inequality.'
ON THE HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 49
Again,
e [ a — 'cjdt)
Hence, if {F — Vjje denotes the valae of (P— l)/e at a time xj(ff — 'sr)
earlier than that of observation, then
n+an'=l(P'i).
e
Hence, in (23),
n + tan2(^r)n'=l(P'l) (26)
where P' is the ratio of the moon's parallax to her mean parallax at a
time tV''57°3 tan 2(^r)/(<7^). The period 57°3tan2(/xr)/(<7w)
may be called ' the age of the parallactic inequality.'
In collecting results we shall write the sum
M2 + So + K2 + N + L + R + T = ;i2.
For reasons explained below we omit terms depending on the rate
of change of solar parallax and declination.
Then, from (15), (16), (18), (19), (23), (24),' (25), (26), we have
h, = ^^ M cos 2(4^ fi) + S cos 2(4^0
cosA^
sin^A, ^' ^ sm^A, ' ^^' *
_sjnacosS cl2r K^ _af tan^A,") sin2(;^^)
ffsin^A^ f/^Vcos 2(ic— /x) /
, COS^A.T,, T .^COS 2^ — ^003 2/\ r>/ 1 \
+ — 2^(P'1) 5 cos2(4/£)
cos^'A, ecoszt
+ (P^l)i?!:iZ^cos 2(;/.,0
cos A_ 1 dP f^ ^j._ Nsec2(ftv) + Lsec2(\fx)
COS A, (T — tn dt
r41f^^'^^«^(^") + ^^""^(^^)^sin2(^;,)
(27)
It may easily be shown, from Schedule B. i., 1883, that in the eqni
librium theory 'it" — If tan2A,=0, and 4M—(N+L)/e=0; hence the
terms depending on rates of change of declination and parallax are small.
This also shows that we were justified in neglecting the corresponding
terms in the case of the sun. Also, since the faster tides are more
augmented by kinetic action than the slow ones, the two functions,
written above, which vanish in the equilibrium theory are normally
actually positive. The formula (27) gives the complete expression for
the semidiurnal tide in terms of hourangles, declinations, and parallaxes,
with the constants of the harmonic analysis.
We shall now show that with rougher approximation (27) is reducible
to a much, simpler form.
The retardation of each tide should be approximately a constant, plus
1885, E
50 REroRT — 1885.
a term varying n'ith the speed. Hence all the retardations may be
expressed in terms of ^ and /x, and
K =[1+ (T,
'hiT^),
a — 1]
(T — 7/
It Is clear that i: differs very little from 4, and that
^At_ 2(M »)_4/t
a a — •Z3 a — i)
The time (^—M)K<^—v) is called 'the age of the tide,' for reasons
explained below, and K — fj, fi — r, not being large angles, do not differ
much from these tangents. Hence the ages of the declinational and
parallactic inequalities are both approximately equal to the age of the
tide.
Let ce, then, denote (if— /i)/((T— ?/), the age of the tide.
Now, as an approximation, we may suppose that heights of the lunar
K2 tide, the N and L tides bear the same ratio to the Mo tide as in the
equilibrium theory ; and that the solar Ko, the T and R tides bear the
same ratio to the S2 tide as in that theory. Then reverting to the nota
tion with J, w, i in place of A, A„ and writing
\ cos iw cos ^1 J
we have
sin^A T'/ pSin^ J^,, cos^A , r^fir cos A
K!'=^^'\UM, ^""^.^N = leBT, "^^L=iefJ/;
sin^ A , cos'' gl cos A , " cos A ^
COS''^u>
Also, since (22) may be written
tan(2u_20=^'''"^'^t:5^2(X^
we have, treating fi — >•, X— /^, /' — « as small, approximately,
£=;ii(;e(ff'=7)=;t(\r).
Also
cos^A iVcos 2i' — L cos 2X _ „,,
— 2" 7, =.3eflf.
cos^ A , cos Ze
Then reverting to mean longitudes, and substituting the age of tide
where required, we find, on neglecting the difference between k and i',
For the lunar declinational term,
2 tan2Ufi/cos2[sa;<T4'] cos 2(^yi;)',
For the solar declinational term,
2 tan2 iw S cos 27i cos 2(^p,0 ;
For the lunar parallactic term,
3eflf cos [s— p — cpfff — ot)] cos 2[;^— yn + ^a'((T — •ar)] ;
ON THE HAEMOMIC ANALYSIS OF TIDAL OBSEKVATIONS. 51
For the solar parallactic term,
3e,(S' cos (h—pi) cos 2[i!'/ — 4].
Then omitting the terms depending on changes of declination and
parallax, we have as an approximation,
7i2=filf fcos 2(>^^) + 2 tan^iJcos 2[s— a'o— £] cos 2(v/'0
+ 3ecos [s— ^ — f[;(<T — ffl)] cos 2[.//— yL( + ((,'((T — ct)]
+ ,S [ 1 +2 tan hw cos 2h + 3e, cos (hp,) 1 cos 2(4/, 4) . . (28)
In the equilibrium theory we have the lunar semidiurnal tide depend
ing on r~3 cos c cos 2i//. Now it is obvious that cos^ introduces a
factor 1 + 2 tan ^Icos 2 (s — ^), and i"^ a factor 1 + 3e cos (s—p). Thus,
if we could have foreseen the exact disturbance introduced by friction and
other causes in the various angles, the formula (28) might have been
established at once ; but it seems to have been necessary to have recourse
to the complete development ia order to find how the age of the tide will
enter.
§ 4. Reference to Time of Moon's Transit.
It has been usual to refer the tide to the time of moon's transit, and
we shall now proceed to the transformations necessary to do so.
cos A /cos^ A, goes through its oscillation about the value unity in
19 years ; it is therefore convenient to write for, say, a whole year,
c^A_3^ ~
(29)
cos' A /
and similarly, N^z=^^'A N
cos^ A ;
7 cos^ A
COS'' A J
"We also observe that K" and Kf, being the lunar and solar parts of
the mean K., tide, and their ratio being 464 (Report, 1883),
K" = 68303K„ K/'=3l697K^ .... (30)
It will also be seen that in all the terms arising from the sun, exceptincr
that in K/', the argument of the cosine is 2(\P,i;). It will be con°
venient, and sufficiently accurate for all practical purposes, to replace
ichy 'C in this solar declinational term Jv'/'.
We shall now proceed to refer the tide to the moon's transit at the
place of observation.
Let a„, h^ be D 's R.A and 's mean longitude at ]) 's transit— say
upper transit, for distinctness. Then the local time of transit is given by
the vamshing of I, and since xl^=t\ha, it follows that the timeangle
ot D s transit (at 15° to the hour) is ci^ — h^.
Now let T (mean solar hours) be the interval after transit to which the
timeangle t refers ; then, since
E2
52 REroKT — 1885.
=[(y'j)^ + «o/'o] + [/'o + 'r]['.o + Tr+('~TV],
For the sake of brevity, put
T = (y<7)T,
so that T is r converted to angle at the rate of 14°'49 per hour. Then
we have
v/.=T(^;^.)r (31)
Similarly putting o^ for 's R. A. at D 's transit, we have
SO that
(la
Then let
^=«oa, (32)*
So that A is the apparent time of ]) 's transit, reduced to angle at 15°
per hour, and we have
;/.,=T + l+('rJ^)r (33)
It is only in the two principal tides that we need regard the changes
of R.A. since B 's transit, and in all the smaller terms we may simply put
The first pair of terms of (28) now become
iLr„cos2[T(^^ay^] + .S'cos2[T + 4+(^^^p)r4],
and these are equal to
lf„ cos 2(T /.) + ,S cos 2(T 4 ^ 
"We may now collect together all the results, and write them in the
form of a schedule.
* It would be better to put
If this bo used the correction (iO) for Q's change of R.A. becomes small.
4 (T — ri
•y — a
ON THE HARMONIC ANALYSIS OF TIDAL OBSERVATIONS.
53
/^
^•^
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Vr
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u
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54 REPOET— 1885.
Definition of symbols : —
a, 5, a„ d, D 's and 's R.A. and declination at moon's transit ;
A=a — Uj, apparent time of 1) 's transit at the port.
57°'3
I' 3) 'sdecl.atthetime(generallyearliertliantransit)r ~ — tan2((v — /i).
JitT
F, P/ the ratio of D 's and 0's parallax to mean paralla,xes.
P' the ratio for )) at the time (generally earlier than transit)
7— tan2(/u — )').
r the time elapsed since ]) 's transit in m.s. hours ; T the same time
reduced to angle at 14°'49 per hour.
A such a declination that cos^ A is the mean value of cos^ o ; A has a
lOyearly pei'iod.
A^ such a declination that cos^ A, is the mean value of cos c,.
e, e, eccentricities of lunar and solar orbits ; a the D 's mean motion ;
«7 the mean motion of the }) 's perigee.
^^^o^io^COS^ A
M IS L cos^A;
M, S, K<i, N, L, T, B the mean semiranges II of the tide.? of those
denominations in the harmonic method. The retardations found by
harmonic analysis are 2^i for M,, 2i^ for S.), 2/c for K.>, 2i' for N", 2\ for L,
and 2^ for T and R. ' " " .
Lastly tan 2e= — ^^ ^ — j ^ 2^ ^q be taken in the same quadrant
'' iVcos2)'ivcos2\ • '■
as 2,'.
§ 5. Synthesis of the Several Terms.
Consider the two principal terms in Schedule IV.
M, cos 2(T  ^0 + ,S' cos 2 (T + ^  .
They may be wiitten in the form
fl'cos2(T^),
where H cos2(n — (j,)=M^ + S cos 2(J. — i+/j),
Hsin2(i^,l>) = Ssm2(A^ + fi).
If we compute f corresponding to the time of moon's transit fi'om the
formula
tan2(^^)^ .Ssin2M^ + ^)
'M, + Scos2(A(+fiy
then (f> reduced to time at the rate of 14°49 per hour is the interval
after moon's transit to liigh water, to a first approximation. The
angle + 90°, similarly reduced, gives the low waters before and after the
high water, and (j!>j180° gives another high water. The high waters
and low waters are to be referred to the nearest transit of the moon.
The height or depression is given to a first approximation by
jff=^/(j\J„2 + g2 + 2iTf„S cos 2 (/x.^)).
OS THE HAKJIONIC ANALYSIS OF TIDAL OBSERVATIONS. 55
This Tariabilitv in the time and height of high water, due to variability
of (,'>, is called the fortnightly or semimenstrual inequality in the height
and interval. The period (:^ — /.i) j (cr — i]) is called ' the age of the tide,'
because this is the mean period after new and full moon before the
occurrence of spring tide.
§ 6. Corrections.
The smaller terms in Schedule IV. may be regarded as inequalities in
the principal terms. They are of several types. Consider a term
£cos2(T/3).
Then
i?cos2CT/3)=5cos2(/30)cos2(T— 0)+5sin2O30)sin2(T0).
Hence the addition of such a term to ffco8 2(T — ^) gives us
(H+dE) cos 2(Tfl<p), where
cH=B cos 2(ft(p),2m(p=Bsm2(i3(l.). . . . (35)
Next consider a term C sin 2(T — /^t). Putting /5=yLi + l, we have
'cR=Csin2(^i<p),2Eo<i>=Gcos2(^(p) . . . (36)
Xext consider a term E cos 2(T4 .4 — i^). Putting /3=^—A, we have
cE=Ecos2(Ai:+<l>),2Hcf=Esin2(Ai:+<i,) . . (37)
Lastly, consider a term JPsin 2(T + J. — 4). Putting /3=^— J. + 7r, we
Lave
cE=Fsm2(A!:+<l>),2El(p=Fcos2(AC + (p) . . (38)
In writing down the corrections we substitute 14'49S^ for c(j), and
introduce a factor so that the times may be given in mean solar hours and
the angular velocities in degrees per hour.
Change of Moon's R.A., Sched. IV.
This is of type (36), and gives
This correction to the height is very small.
Cliancje of Sun's R.A., Sched. IV.*
This is of type (38), and gives
(89)
(40)
* "With the value of A suggested in footnote to (.32) {a  da, j dt)r becomes
[((p/i)tr(<p^a, jdinv)] I iy — <r) at high water. This is obviously very small.
56
REPORT — 1885.
Moon's Declination, Sclied. IV.
This is of type (35), and gives
oif=^^5^i^^^^683Ji2Cos2(^— .ji)
sin'' A/
.^^^^.gj,j,cos^a^cos2_A
sin^ Aj
Sun's Declination, Sclied. IV.
This is of type (37), and gives
•6835 sin 2 (».— </.)
(41)
cH=^^^lIlZ^2!l^ 317 K2Cos2(A( + <)>) '
3f = lh977^5^!A:i^£?!^' .317 ^ sin 2(Ai: + (p)
sin''' A, M
(42)
Change of Moon's Declination, Sched. IV.
This is of type (36), and gives
SH='^^^l^ da 7 683 K, Mts^n^A,) sin 2(;.^))
ffsm^^, dt\cos2{t:fi) 'J ^^ [(4.3
sin ? cos 2 cU f •683/1, ^ '
U=  P977
(tH sin^ A
Moon's Parallax, Sched. IV.
This is of type (35), and gives
, dt \co92{kii) 7 ^^ ^')
cB={p'^iy^
N„ cos 2t' — L. cos 2\
e cos 2£
cos 2(£ — 0)
t<=lh977(P^l)^'° "°" ^'^° ^"" '^^ sin 2(£<^)
i/e cos 2£
Sun's Parallax, Sched. IV.
This is of type (37), and gives
afl"=(P,l)^^ cos2(44+f)'
ct= lh977(P,I)^^ sin 2(^C + «/')
Change of Moon's Parallax, Sched. IV.
This is of type (36), and gives
(44)
(45)
m=^^ ^f414 ^°^"^^<^") + ^°^""^^^^) Uin2(uri,)l
1977 dP^^^^^_ N^sec2(^r) + L^.ec2(X,) ^ '
{a—'m)H dt\ e J J
H=
(46)
The lunar corrections involving sines are small compared with those
involving cosines.
To evaluate these corrections we must compute r from f reduced to
time at 14°'49 per hour.
In the right ascenaionalterms, da/dt and a are to be expressed in
degrees per hour, da/dt is the hourly change of ))'s H.A. at time of
B 's transit, and dajdt is the hourly change of © 's R.A. at time of D 'b
transit.
ON TUE HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 57
Similarly, dcjdt is to be expressed in degrees, if a be in degrees.
c', P' can be found for the antecedent moments, 57'''3 tan 2(k — ^()/2o,
and 57°'3 tan 2(/i — i')/(t — ■or), before the time t.
§ 7. The Diurnal Tides.
I shall not consider these tides so completely as the semidiurnal ones,
although the method indicated would serve for an accurate discussion, if
it be desired to make one.
The important diurnal tides are Ki, 0, P.
From Schedule B ii., 1883, we have
sinlcosHI M'cos [f + 7.,.,2(.0 + iU//].
sm w cos' ^w cos'' ^^
By (9) the coefficient is sin 2^ /sin 2^„ and we shall put, as in the
case of the semidiurnal tides,
bin ZA^
Then, since t + h=^ + a,
(0)=J/o' cos [4'+(a + ''o)2(s0+i'^A'']
=MJ cos ii, for brevity {'^7)
Again, from Schedule C, 1883,
(P) = ,S'' cos [iZi + K;"] ;
Then let x=2(s/0 + 'o2^4' + m'> and we have
(?) = «' cos (il + x) (48)
Whence
(0) + (P) = [lfo' + <S' cos xl cos aS' sin x sin fi.
If we pnt,
E' cos {i^'<i>')=MJ + S' cos X
H'sin (^'.^')='S'Binx.
(0) + (P)=fi' cos (O + m'^')
=ir'cos[>/. + («>02(s^)+i7rf] . (49)
Where
R'=s/ {ilA'2 + 6"2 + IM^S' cos xl
and tan (a'd,')= ^l^^'^J^ —
'^^ ' ^ 34' + /S"cosx
(50)
The rate of increase of the angle x is twice the difierence of the mean
motions of the moon and sun, but it would be more correct to substitute
for s and li the true longitudes of the bodies. It follows from (50) that
^' has a fortnightly inequality like that of <l>.
\p is very nearly equal to T, and where the diurnal tide is not very large
we may with sufficient approximation put
(arj2(s0=(s,0.
So that with fair approximation
(0) + (P)=fl'cos[T(s0 + 7r^'] . . . (51)
58 iiErouT — 1885.
The synthesis of the two parts of the Kj tide has been performed in
the harmonic method (Report, 1883), and we have
(K,) = fi7iri cos (t + h—y' — hTr — i:^).
Then, writing iJ{i=K„, we have
(K,)=7v„ cos (T + a.''i7r/.i) .... (52)
We have next to consider what corrections to the time and height of
high and low water are necessary on account of these diurnal tides.
If we have a function
A=I7 + B'cos2(T./)) + B"iCOs(«T/3),
where n is nearly equal to unity, and H^ is small compared with H; its
maxima and minima are determined by
sin 2(Tf/>)= ^ sin (nT /3).
If T=To be the approximate time of maximum, and To + oTq the true
time, then, since the mean lunar dayis24"84 hours, and the quotient when
this is divided by Stt is 0'^'988, we have in mean solar hours,
oT,= 0988^^sin(7iT,/3) "i
And the correction to the maximum is
■ ^cH=E, cos (nT,l3)
Again if T=Ti be the approximate time of minimum, and Tj + cT,
the true time, then
(53)
cTi ^0988^ sin (7iTi/5)
(54)
And the correction to the minimum is
m=Hi cos (nTy ft)
In the case of the correction due to (0) + (P))''' is approximately
1 , and for the correction due to Ki, n is approximately l\
y — <T y — a.
§8. Direct Synthesis of the Harmonic Expression for the Tide.
The scope of the preceding investigation is the establishment of the
nature of the connection between the older treatment of tidal observa
tion and the harmonic method. It appears, however, that if the results
of harmonic analysis are to be applied to the numerical computation of a
tidetable, then a direct synthesis of the harmonic form may be preferable
to a transformation to moon's transit, declinations, and parallaxes.
Semidiurnal Tides.
"We shall now suppose that M^ is the height of the M^ tide, augmented
or diminished by the factor for the particular year of observation, accord
ing to the longitude of the moon's node, and similarly K^ generically for
the augmented or diminished height of any of the smaller tides. As
ON THE IIARMOXIC ANALYSIS OF TIDAL OBSEKYATIONS. 09
before, let 2/j, 2^' bo the lags of Mo, So ; and 2v, generically, the lag of
the K tide.
Let 6=l + hsy^ + E.
Then 6 might be defined as the mean moon's hourangle, the mean
moon coinciding with tlie true, not at Aries, but at the intersection.
Let the argument of the K tide be written genericallj' 2\_0 + u~i:'].
Then
h,=M„eos2(6fi) + Scos2[8 + sli + v^^!:]+K,cos2[0 + uK'\
. . . (55)
If we write
So ^=4 ''o + s,
and
E cos 2 (ju  f) =M^ + S cos 2[sJi ; „ + ^, ]
Hsin 2(^Lf) = S sin 2[..7i4o + A'].
the first two terms of (55) are united into
Hcos2(efi>) (56)
with fortnightly inequality of time and height defined by
tan2(,^)== S.in2(shi:^ + ,)_^
E= v/ [ ir,2 + ,s2 + 2MS cos 2 (s  7.  f „ + ^) ] )
The amount of the fortnightly inequality depends to a small extent
on the longitude of the moon's node, since (^ 3"tl M^ are both functions
of that longitude.
For the K tide we have
Ka cos 2(d + n — K)=K^ cos 2(u — K + (p) cos 2((i — </.)
— Ko sin2(u — K + (p) sin 2(6 — (p).
Hence
2H"= K^ cos2(u — K+(j)) ]
K .... (58)
cf=^sm2(u. + ^) )
It is easy to find from the Nautical Almanac (see Moon's Libration)
the exact time of mean moon's transit on any day, and then the successive
additions of 12''4206U1 or 12^ 25™ 14sl6 give the successive upper and
lower transits. The successive values of 2(s — h) may be easily found by
successively adding 12°6180o6 to the initial value at the time of the first
transit of the mean moon, and may be obtained from the table of the
fortnightly inequality for each value of 2(.s— 7i).
The function ti is slowly varying, e.g., for the K2 tide 2u=2(!i — t,)
+ 2(i'o — )'"), and the increment of argument for each 12*'420G01 may be
easily computed once for all, and added to the initial value.
In the case of the diurnal tides it will probably be most convenient to
apply corrections for each independent]}, following the same lines as those
sketched oiit in § 5.
The corrections for the over tides M4, S4, &c., and for the terdiurnal
60 KEPOBT— 1885.
and quaterdiarnal compound tides, would also require special treatment,
which may easily be devised.
At ports, where the diurnal tide is neaily as large or lai'ger than the
semidiurnal, special methods will be necessary.
Although the treatment in terms of mean longitudes makes the cor
rections larger than in the other method, yet it appears that the compu
tation of a tidetable may thus be made easier, with less reference to
ephemerides, and with amply suflBcient accuracy.
Report of the CoTnviittee, consisting of Mr. Robert H. Scott
{Secretary), Mr. J. Norman Lockyer, Professor Gr. Gr. Stokes,
Professor Balfour Stewart, and Mr. Cf. J. Symons, appointed
for the purpose of cooperating with the Meteorological Society
of the Mauritius in their propjosed publication of Daily
Synoptic Charts of the Indian Ocean from, the year 1861.
Dratvn up by Mr. E. H. Scott.
The Committee have the honour to forward, for the inspection of tlie
members of the Association, a cop}' of the Charts for the month of March
1861, with some specimens for January of the same year, and the com
plete number for February which appeared some years ago. These docu
ments have recently arrived from the Mauritius.
As the work has now made decided progress, the Committee have
a])plied for and obtained the grant of 50^. placed at their disposal by the
General Committee.
As soon as the requisite documents are received from Dr. Meldrum,
the Committee will submit a formal account of their expenditure with
the necessary vouchers.
Report of the Committee, consisting of Mr. James N. Shoolbred
(Secretary) and Sir William TH0MS0^', appointed for the re
duction and tabidation of Tidal Observations in the English
Channel, made ivith the Dover Tidegauge ; and for connecting
them tvith Observations onade on the French coast.
Your Committee herewith beg to submit the High Water and the Low
Water Observations for the years 1880, 1881, 1^82, and 1888, obtained
from the records of the selfregistering tidegauges at the ports of Dover
and of Ostend respectively.
The observations, in order to facilitate comparisons, are reduced to
Greenwich time and to the common daturaplane of 20 feet below the
Ordnance datum of Great Britain.
As the reduction and tabulation of the present series of tidal observa
tions has proved a longer operation than was anticipated, there has been
hardly sufficient time to consider the best form in which those observa
tions should be placed for comparison, nor for the more suitable deductions
which may be drawn from such comparison.
Your Committee, therefore, request to be reappointed.
ON STAXDABDS OF WniTE LIGHT. 61
Report of the Comviittee, consisting of Professor Gr. Forbes (Secre
tary), Captain Abxey, Dr. J. Hopkixsox, Professor W. Gr. Adams,
Professor Gr. C. Foster, Lord Rayleigh, Mr. Preece, Professor
Schuster, Professor Dewar, Mr. A. Vernon Harcourt, and Pro
fessor Ayrton, appointed for the purpose of reporting on Stand
ards of White Light. Drawn up by Professor Gr. Forbes.
The experimental work of tlie Committee during the past year has not
been extensive, as they had no funds at their disposal for expei'imental
research, and they have been chiefly occupied with reviewing what has
been done in the past and laying plans for future operations.
Lord Rayleigh has constructed an instrument which he calls a mono
chromatic telescope, by means of which the illuminated screens of a photo
meter may be examined, allowing light only of one definite colour to pass.
It was hoped by Lord Rayleigh that experiment might show that, with
some suitably chosen colour, this instrument, nsed with any ordinary
photometer, would, in comparing lights of different intensities and tem
peratures, give to each a candlepower which would be sufficiently
accurate to represent for commercial purposes the intensity of the light.
The Secretary has made some experiments at the Society pi Arts, where
he was kindly permitted to use the secondary batteries and glow lamps ;
but the results so far are not definite enough to justify their publication.
Mr. Vernon Harcourt has been engaged on an investigation on the
barometrical correction to his pentane standard, and on another con
cerning the possibility of using lampshades as a protection from air
currents. His researches are communicated independently to the meeting.
Captain Abney and General Testing have continued their observations
on the intensity of radiations of different wavelengths from incandescent
carbon and platinum filaments at different temperatures, which will go far
to assist the Committee in their work.
Other isolated experiments have been made by members of the Com
mittee, which will be published in due course.
Most of the members have examined the experiments of the Trinity
Board at the South Foreland.
Existinrj Standards.
A consideration of existing standards convinces the Committee that
the standard candle, as defined by Act of Parliament, is not in any sense
of the word a standard. The French ' bee Carcel ' is also liable to vari
ations ; and with regard to the molten platinum standard of Violle, it
seems that the difficulty of applying it is so great as to render its general
adoption almost impossible.
With regard to the socalled standard candle, the spermaceti em
ployed is not a definite chemical substance, and is mixed with other
materials, and the constitution of the wick is not suflSciently well defined.
Hence it is notorious that interested parties may prepare candles con
forming to the definitions of the Act which shall favour either the pro
ducer or consumer to a serious extent. In view of these defects of the
standard candle, it is a matter of great importance that a standard of
light should be chosen which is more certain in its indications.
The Committee have looked into the merits of different proposed
standards, and the majority feel satisfied that, for all the present com
G2 REroRT— 1885.
mercial requirements, the pentane standard of Mr. Yernoii Harcourt —
since it lias no wick and consumes a material of definite chemical com
position — when properly defined, is an accurate and convenient standard,
and gives more accurately than the socalled standard candle an illumi
nation equal to that which was intended when the Act was framed.
Yet the Committee, while desiring to impress the Board of Trade and
the public with these views, do not feel inclined at present to recommend
the adoption of any standai'd for universal adoption until, further in
formation on radiation having been obtained from experiment, they may
learn whether or not it may be possible to propose an absolute standard,
founded, like electrical and other stpndavds, on fundamental units of
measurement — a standard which, for these reasons, would be acceptable
to all civilised nations. They are, howevei', inclined to look upon the
pentane lamp as an accurate means of obtaining an illumination to replace
the socalled standard candle.
Froposed Experimental Hesearcltes.
Radiation is measured as a rate of doing work, and consequently
radiation might be measured in watts. The illumination (or luminous
effect of radiation) depends partly upon the eye, and is a certain function
of the total radiation. This function depends upon the wavelength of
the radiation, or on the different wavelengths of whicli the radiation, if
it be compound, is composed. This function of the radiation perceived
by the eye is partly subjective, and varies with radiations of different
wavelengths and with different eyes. Thus the illumination cannot, like
the radiation, be expressed directly in ab.^olute measurement. But the
connection between the illumination and the radiation can be determined
from a large number of experiments with a large number of eyes, so as to
get the value of the function for the normal liuman eye. This function,
however, is constant only for one source of light, or, it may be, for sources
of light of the same temperature. It appears, then, that, in the first
instance at least, a standard should be defined as being made of a definite
material at a special temperature.
The energy required to produce a certain radiation in the case of a thin
filament of carbon or platinumiridium heated by the passage of an electric
current can be easily measured by the ordinary electric methods, and the
radiation may be measured by a thermopile or a bolometer, which itself
can be standardised by measuring the radiation from a definite surface
at 100° C, compared with the same at 0° C. The electric method
measures the absorption of energy ; the thermopile measures the total
radiation. These two are identical if no energy is wasted in convection
within the glass bulb of the lamp, by reflection and absorption of the glass,
and by conduction ffom the terminals of the filament. Captain Abney and
General Festing have come to the conclusion that there is no sensible loss
from these causes. The Committee propose to investigate this further.
This constitutes a first research.
No research is necessary to prove that vvith a constant temperatui'e of
a given filament the luminosity is proportional to the radiation, because
each of these depends only upon the amount of surface of the radiating
filament. It will be necessary, however, to examine whether with
different filaments it be possible to maintain them at such temperatures as
shall make the illumination of each proportional to the radiation. This
will be the case if spectrum curve^', giving the intensity of radiation in
ON STANDAKDS OF WHITE LIGHT. 63
terms of tl\c wa%elengtli when made oiTfc for tbe different sources of light,
are of the same form. Thus a second research must be undertaken to
discover whether the infinite number of spectrum radiation curves, which
can be obtained from a carbon filament by varying the current, are
identical in form wiion the filament is changed, but the material remains
so far as possible of constant composition.
It will be an object for a later research to determine whether, when
the radiation spectrum curve of any source of light has been mapped, a
similar curve can be found among the infinite number of curves which
can be obtained from a single filament.
The next stc]) proposed is to e.\amine a large number of carbon or of
platinumiridinm filaments, and to find whether the radiation spectrum
curve of different specimens of the same material is identical when the
resistance is changed in all to x times the resistance at 0° C. If this
law be true, a measurement of the resistance of the filament would be a
convenient statement of the nature of the radiation curve. If, then, a
number of filaments were thus tested to give the same radiation spectrum
curve, their luminosities would in all cases be proportional to their
radiations, or (if there be no loss in convection, conduction, absorption,
and reflection) proportional to the electrical energies consumed.
Thus it might be hoped to establish a standard of white light, and to
dctlneit somewhat in the following manner: — ^4 zinit of light is ohtained
from a straigJit carbon fila'inent, in the direction at right angles to the middle
of the filament, when the resistance of the filament is onehalf of its resistance
at 0° C, and when it consumeslO^ C.G.S. units of electrical energyper second.
Since Mr. Swan has taught ns how to make carbon filaments of
constant section by passing the material of which they are composed
throuoh a die, it is conceivable that another absolute standard should be
possible — viz., a carbon filament of circular section, with a surface, say,
TiTij ^l centimetre, and consuming, say, 10^ C.G.S. units of energy per
second.
Whether such standards are possible or not depends npon the experi
ments of the Committee. The probability of success is suflBcient to render
these experiments desirable.
Proposed Later Experimental Researches.
Should these hopes be realised, and an absolute standard of white
light thus obtained of a character which would commend it to the civilised
world, it would then become an object of the Committee to find the ratio
of luminosity when the radiation spectrum curve of the standard filament
is varied by varying the current, and consequently the resistance of the
filament.
Thus, by a large number of subjective experiments on human eyes, a
multiplier would be found to express the illumination from the standard
lamp, with each degree of resistance of the filament.
A reseai'ch, previou.sly hinted at, would then be undertaken — viz., to
find whether the radiation spectrum curves of all sources of illumination
agree with one or other of the curves of the standard filament. It is not
improbable that this should be the case except for the high temperature
of the electric arc.
Should this be found to be true, then photometry would be very
accurate, and the process would be as follows: — Adjust the standard fila
ment until its radiation spectrum curve is similar to that of the lijht to he
64 REPORT — 1885.
compared. (This would probably be best done by obsei'ving tlie wave
length, of the maximum radiation, or by observing equal altitudes on
either side of the maximum, the instruments used being a spectroscope
and a line thermopile or a bolometer.) The total radiation of each is then
measured at equal distances by the thermopile. The resistance of the
filament is measured, and its intensity in terms of the unit of white light
obtained therefiom by the previous research. The luminosity of the
compared source of light is then obtained directly.
The Committee desire to be reappointed, and to enable them to carry
out the researches indicated they ask for a grant of 30^.
Second Report of the Committee, consisting of Professor Balfour
Stewart (Secretary), JNIr. J. Knox Laughton, Mr. Gr. J. Symons,
]Mr. R. H. Scott, and Mr. Johnstone Stoney, appointed for
the purpose of coopjerating luith Mr. E. J. Lowe in his pjroject
of establishing a Meteorological Observatory near Chepstow on
a permanent and scientific basis.
Since theh reappointment in 1884 this Committee have met twice, and
have placed themselves in correspondence with Mr. Lowe.
In this correspondence the Committee have expressed their opinion
that the establishment of a permanently endowed meteorological observa
tory ou a good site, such as that of Shire Newton, is a matter of undeniable
scientific importance.
The attitude whicli the Committee have taken will be rendered appa
rent by the following letter written by their Secretary to Mr. Lowe : —
' The Committee request me to point out to yoa that the main feature
of your proposal, which interests the British Association and the scientific
public generally, is the prospect which it holds out of the establishment
o? a permanent institution by means of which meteorological constants
could be determined, and any secular change which may take place
therein in the course of a long period of years be ascertained. It will be
for you and the local authorities to decide what amount of work of local
interest should be contemplated, and on this will the scale of the observa
tory mainly depend. The Committee are therefore unable to say what
amount of capital would be required. They would point out four con
ditions which they hold to be indispensable : —
'1. The area of ground appropriated should be sufficient to ensure
freedom from the effect of subsequent building in the neighbourhood.
' 2. A sufficient endowment fund of at least 150L annually should be
created.
' 3. The control should be in the hands of a body which is in itself
permanent as far as can be foreseen.
' 4. The land for the site shall be handed over absolutely to the above
mentioned governing body.'
This communication from the Committee is now under the considera
tion of Mr. Lowe and his friends, but until the precise amount of the
local meteorological requirements is ascertained and further progress is
made in the scheme the Committee consider that they would not be justi
fied in any more prominent action than that which they have already taken.
They would request their reappointment, and that the unexpended sum
of 2hl. be again placed at their disposal.
ON COMPARING AND EEDUCING MAGNETIC OBSERYATIONS. 65
Report of the Committee, consisting of Professor Balfour Stewart
{Secretary), Sir W. Thomson, Sir J. H. Lefroy, Sir Frederick
Evans, Professor Gr. H. Darwin, Professor Gr. Chrystal, Professor
S. J. Perry, Mr. C. H. Carpmael, and Professor Schuster,
appointed for the purpose of considering the best means of
Com/paring and Reducing Magnetic Observations. Brawn up
by Professor Balfour Stewart.
In presenting their report to the Britisli Association the Committee
would begin by referring to the appendix, in which are embodied sug
gestions of great value which they have received from men of science at
home and abroad. The Committee desire to express their thanks to the
authors of these contributions.
While a final discussion of these communications cannot be attempted
in this first report, it is nevertheless evident that magneticians are not
agreed as to the best method of determining absolutely the solardiurnal
variations of the three magnetic elements — that is to say, the diurnal
variation resulting after the elimination of all disturbed obsei'vations.
The point in dispute is the method of distinguishing and separating the
disturbed from the undisturbed observations. On the whole, the feeling
is against the method of Sabine, on account of the arbitrary nature of his
separating value.
An alternative method has been proposed by Dr. Wild, Director of the
Central Russian Observatory (Appendix, No. VII.). This method seems
to be in some degree analogous to that pursued at Greenwich (Appendix,
No. IX.). Dr. Wild selects those curves which appear to the eye to be
free from the shortperiod irregularities characteristic of disturbances,
and considers the results obtained from their measurement to embody a
trustworthy representation of the solar diiirnal variation for the time and
place in question. He finds a remarkable uniformity and simplicity of
type in the variation as given by the difi"erent selected curves.
While the Committee recognise in this a method which may ultimately
meet with general acceptance, they think there are various points con
nected with it which require investigation.
In the first place, it would be desirable to prove, by means of an
exhaustive discussion of some one element — as, for instance, the declina
tion — to what extent curves selected by the eye do, as a matter of fact,
present this uniformity and simplicity of type.
There are abundant materials available for this purpose at the Kew
Observatory, and it is hoped that through the kindness of the Kew
Committee this point may eventually be settled.
Again, it would be desirable to ascertain whether the apparently
normal days at one station coincide with those at another ; and, if so,
whether there is a definite or nearly definite relation in type and range
between the corresponding smooth curves of two widely separated stations
of not very dissimilar latitude.
This point will form one of the subjects of a discussion undertaken by
Sir J. Henry Lefroy, who proposes to compare the curves of Toronto and
those of Greenwich together for the years 184953.
1885. F
66 REPORT — 1885.
The Committee are of opinion that these are steps \vhich might at
once be taken, so as to push on this part of the subject.
The Committee would call attention to the completeness of the mag
netical information which is given by the present method of publication
adopted by the Astronomer Royal. He now gives, in addition to the
mean values of the magnetic elements for each day and the mean diurnal
curves for each month, the amplitade of the diurnal curve for each day,
and particulars of all disturbances, small as well as large. (See Appendix,
No. IX.)
Until a method is generally accepted for determining the normal solar
diurnal valuation, it seems prematuie to raise any discussion on the best
■way of estimating disturbances, since these cannot well be measured
except from the basis of such a normal.
The Committee would, however, allude to various investigations,
chiefly connected with disturbance, which are being undertaken by some
of its members. The thought seems generally to have occurred that dis
turbances may denote the method by which the earth rights itself with
respect to the magnetic forces acting upon it (see Appendix, No. II., para
graphs 11 and 12), and this idea underlies the various researches about
to be named.'
The first of these is that already mentioned as having been taken up by
Sir J. H. Lefroy, with the concurrence of the Astronomer Royal — namely,
a comparison oi magnetic movements photographically recorded at
Toronto and Greenwich in the years 184953. Stations so far asunder
(3,100 miles), and on different continents, appear calculated to throw
light on many questions which are not much advanced by compaiison of
stations in geographical proximity.
The following are i^ri ma facie conclusions which may require modifica
tion when the work has been gone through, but which already seem to
have a bearing on the physical explanation of the phenomena : —
a. A similar state of magnetic weather, so to speak, prevails generally
at both stations, so that where numerous or extensive deviations from
normal regularity occur at the one, there is generally something corre
sponding at the other.
h. The correspondence very seldom amounts to similarity of movement
or identity of time.
c. The changes of declination at Toronto are more rapid than at
Greenwich. This is especially observable about the time of the morning
easterly extreme. Bold sweeping curves with a long time measure are
much less common at Toronto than at Greenwich, and can seldom be
identified.
d. On the other hand, shocks of small angular amount breaking a
uniform line are often capable of identification, and are simultaneous,
or nearly so, at both stations.
e. Although the declination was westerly at both stations, the move
ments of disturbance are very frequently, probably usually, in opposite
directions at any given time — easterly at Greenwich, or decreasing the
absolute declination, when they are westerly, or increasing it, at Toronto.
/. The same days would generally be selected to form normal curves
at both stations.
> A similar idea seems to have occurred to Dr. Wild (see footnote to his communi
cation, Appendix, No. VII.).
ON COMPARING AND EEDUCING MAGNETIC OBSERVATIONS. 67
g. Sliglit auroral displays in Canada generally produce a mai'ked effect
at Toronto, but none at Greenwich.
h. It is not easy to answer the question whether a state of disturbance
succeeding one of calm begins or ends at the same time at both stations,
neither beginning or ending being, in general, sufficiently definitely
marked.
i. It appears impossible to assign a value based on angular movement
alone which will be a valid test, whether such movement is due to dis
turbing causes or not.
j. Angular movements at Toronto appear to be larger than at Green
wich, the magnets being (in 184950) similar — namely, 2 feet in length.
The second research is by the Rev. S. J. Perry and Professor Stewart,
who, with the sanction of the Kew Committee, are engaged in a com
parison of the simultaneous disturbances of the declination at Stonyhurst
and at Kew. Calhng the first S, and the second K, they have obtained
the following preliminary results, which may, however, ultimately require
some modification : —
(1) S is always greater than K, or the ratio ^ is always greater than
unity.
• (2) This ratio appears to depend in some way on the duration of the
disturbance.
(3) But not, as far as can be seen at present, upon its magnitude.
A third research is by Professor Stewart and Mr. W. Lant Carpenter,
who are making a preliminary trial of four years of Kew declination dis
turbances (separated by Sabine's method), in order to ascertain whether
the aggregate daily disturbance depends upon the relative position of the
sun and moon, and also whether it is affected by meteorological storms.
The following provisional result has been obtained from the years 187073
in which the lunation is divided into 8 parts, (0) denoting new, and (4)
full moon.
Mean Daily Aggregate of Disturbance of Declination at Kew}
(Unit xo^^'b of an inch, measured on the curve.)
(0)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
111
114
104
95
83
94
107
101
The Committee desire to draw the attention of magneticians to the
urgent need of obtaining more accurate knowledge than we possess at
present of the daily variation of the vertical force. No attempt to fix
the cause of the daily variation can be made until the daily variation of
each component of the magnetic force is known.
In conclusion, the Committee desire their reappointment, with the
addition to their number of Captain Creak and of Mr. G. M. Whipple,
Director of the Kew Observatory, and they would request that the sum
of 50Z. should be placed at their disposal, to be spent as they may think
best on the researches mentioned in this report.
' The late Professor J. Clerk Maxwell was, it is believed, the first to suggest that
the lunardiurnal variation of the earth's magnetism maybe caused by distortion, and
Dr. Schuster has suggested that, if there is found to be a relation between magnetic
disturbances and atmos]pheric storms, it may be of the same nature.
f2
68 REPORT — 1885.
APPENDIX.
Suggestions for the Committee on Magneticcd Reductions.
I. By Professor Balfoue Stewakt, F.R.S.
1. The following suggestions are founded on the methods proposed by
several magneticians, including Sabine, Broun, Lefroy, Capello, and Buys
Ballot. To Senhor Capello I am especially indebted for the trouble he
has taken in explaining his views, with which these suggestions are
almost identical.
2. The measurements derived from selfrecording magnetographs may
be used for two purposes, the first being to ascertain the solar diurnal
variation, by which name we designate that variation which is exhibited
by comparatively undisturbed observations. The second of these pur
poses is to ascertain the laivs ivliich regulate Jisturhances. Now disturbances
may act in two ways. First, they may exhibit a diurnal variation different
from that of the undisturbed observations, which we may call the dis
hcrhance diurnal variation ; and, secondly, they may exalt or depress the ^
day's value of the particular element in question.
As a matter of fact I believe they act in both these ways. It appearsi
to me that it is of very great importance that these two effects of disl
turbance should be exhibited and studied togertier, and yet not impro
perly mixed up with one another.
3. Let me explain my meaning with reference to the method of Sabine,!
■which I believe to be, in many respects, an excellent one. Sabine did
very great deal in finding out and exhibiting the diurnal variations of the'
disturbed and undisturbed observations, but he did not greatly study,
along with these, the effect of disturbances in altering the daily mean
values of an element, so that it was reserved for Broun to discover that
there were changes in the daily values of the horizontal force which were
practically simultaneous at the various stations of the globe. Let us fiist
of all consider the hourly values of declination, as this element presents
fewest difficulties.
Declination,
4. Here, I imagine, the first thing is to determine the solar diurnal
variation, or that presented by the comparatively undisturbed observations,
and for this purpose I fail to see a better plan than that proposed by
Sabine. This method may be described as follows :
5. Suppose that we have hourly observations at a station, then, first
of all, we should arrange these into monthly groups, each hour by itself.
We should then reject, as disturbed observations, all those which differ
by more than a certain amount from their respective normals of the same
month and hour, the normals being the hourly means in each month after
the exclusion of all the disturbed observations. For the purpose of
ascertaining the true solar diurnal variation, it seems probable that a
considerable choice might be allowed in selecting the separating value
implied in the above process, one value serving, for tliis pii^rpose, probably
as well as another a little above or below it.
6. Perhaps under ordinary circumstances a value which will exclude
as disturbed about onetwentieth of the whole body of observations will be
found convenient.
7. Let us now imagine that we have determined by this process
ON COMPARING AND REDUCING MAGNETIC OBSERVATIONS. 69
the undisturbed normpJs for eacli hour, for each month. I agree with
Sir J. H. Lefroy in thinking that the best plan of investigating disturb,
ances is, in the first place, to obtain the various departures of individual
observations from their respective normals for that month and hour. It
would be desirable to embody these departures in a fresh table, in which
(except for those who are colourblind) the negative departures might be
given in red ink and the positive in black.
8. In this table, at the right of the twentyfour departures for the
various hours of the day, I should represent the mean departure for that
whole day either in red or black. It would thus be seen, at a glance,
whether the average of the whole day was affected by disturbance, in
what direction, and to what extent.
9. It is here assumed that, during the month in question, no alteration
of scale value or other instrumental change has taken place. Never
theless at stations which have a considerable secular variation of decli
nation, and for which this is known, it might be desirable to introduce,
say to the extreme right, a column embracing a small residual correction,
applicable to each day's departures, on account of secular change.
10. I imagine that a monthly table, constructed after the method
which I have described, will afford a full and satisfactory basis for the
discussion of disturbances.
11. It is probable that the smaller departures will follow the law of
the ordinary solar diarnal variation, and, in that case, there should be as
many Ijlach as red sums in these minor departures, or, in other words, the
algeiaraic sum of these should be zero, while the sum taken without
respect to sign or colour should represent the amount of oscillation or
disturbance obeying the ordinary law, this being a point which it is of
interest to determine. No doubt the larger disturbances will obey some
other law, and it will be necessary to separate them into two categories,
those increasing and those diminishing the declination. Here I should
follow Dr. Buys Ballot's advice, and allow the observations themselves to
determine where the one law ends and the other begins. It is just possible
that sometimes the day's mean may be decidedly different fi'om what it
ought to be, and yet the diurnal variation for that day be as nearly as
possible the same as for undisturbed observations. A table, such as that
now described, will show, at a glance, whether such a state of things ever
takes place.
Horizontal and Vertical Force.
12. The horizontal and vertical force magnetographs are different
from the declination magnetograph, inasmuch as their indications are
affected by change of temperature, by loss of magnetism, and possibly,
in the case of the vertical force instrument, by other circumstances not
well understood.
13. It will be noticed that, in treating the declination results by
Sabine's method, we perform oar operation upon the individual declina
tion values. Now it might be said, why not (your object being to find
the solar diurnal variation) take the dej^arture of the individual hours of
a day from the mean of that day, and treat each month's departures by
Sabine's method ?
14. The reply would be that the mean of a day is more likely to be
affected by disturbance than the monthly mean of an hour. For disturb
ances, when they come, generally affect several consecutive hours, thus
70 REPORT — 1885.
altering the daily mean, but, on the other hand, they are less likely to
affect the same hour during consecutive days. Were we able to obtain
daily means of declination, unaffected by disturbance, it would be better
to adopt this method of treatment, because it would obviate the intro
duction of any residual correction due to the progress of secular change
or annual or semiannual variation. Now in the force magnetographs
the case is different. Here there is a certainty that some — perhaps even
a considerable — change will be produced in the values belonging to a given
hour in the course of a month from instrumental changes alone, so that
treating the observations after the manner pursued with the declination
might lead to erroneous results.
15. On the other hand, if there were no disturbance, the difference of
the various hourly observations of a day, from the mean of that day,
would give us a good indication of the solar diurnal vaiiation, provided
the diurnal range of temperature was inconsiderable, as is generally the
case for selfrecording instruments.
16. These remarks render it manifest that some method of obtaining
probable values of the undisturbed daily means is, in the case of the
force instruments, of vital importance, and Senhor Capello has adopted
a method of this kind in his treatment of his force observations. I would
venture to remark that the most unexceptionable basis upon which to
determine the undisturbed daily means of horizontal and vertical force
would seem to be given by the information already assumed to be obtained
from the declination magnetograph for the same month.
17. Here, as a result of the application of Sabine's method, we have
rejected a certain number of hourly observations as disturbed. Now let
us reject, as a preliminary step to something more complete, precisely the
same hourly observations of the horizontal and vertical force as being, in
all probability, disturbed, and make use of the remainder, or of that part
of the remainder which represents whole, or nearly whole, days free from
disturbance, to aid us in determining, by a curve, the most probable values
of the undisturbed daily means. I here assume that there is no sudden
jump in the month's readings from change made on the instrument or
any other cause ; if there be such, the portions before and after the jump
will have different values, and must be treated by appropriate methods
which need not here be discussed. Suffice it to say that, by rejecting
from the month's observations those hours which were separated as dis
turbed in the declination, and treating the remainder in the manner
suggested, we obtain, aided, perhaps, by a slight equalisation, numbers
representing very nearly the undisturbed daily values of the records
given by the insti'uments.
18. Having obtained these, our next operation is to obtain the hourly
differences from each day's undisturbed mean. These differences, so
obtained, we i^ropose to treat in the same manner in which we treated
actual declination observations. It is, therefore, to these differences that
Sabine's process should be applied, so that ultimately, when we have
applied it, we shall obtain those departures of each hour from the daily
mean which characterise undisturbed observations — in other words, we
obtain the solar diurnal variation.
19. Having obtained this, we have at once the means of obtaining a
table similar, in all respects, to that which we have recommended for the
declination. For instance, if the departtire of a given hour of a given
day from the undisturbed mean of that day were + 9 whereas, according
ON COMPAEING AND KEDUCINa MAGNETIC OBSERVATIONS. 71
to the solar diurnal variation for undisturbed observations, it should have
been +3, the number +6 would be inserted in the table, and so on.
20. It will be seen at once that we shall be able to ascertain by the
method now described, if disturbance (as Broun supposed) alters the
daily average values of the horizontal force. For in the horizontal force
instrument any comparatively short period change of average daily value
is hardly likely to be caused by instrumental alteration, but is most pro
bably due to magnetic causes, more especially if the same change take?
place simultaneously at various stations.
There are, however, moie serious difficulties connected with the
vertical force instrument, but into these I cannot now enter.
II. By Sir J. Hexet Lefeot, K.C.M.G., F.R.S.
1. The statement of the question appears to assume that the first, or
chief, object of continuous automatic registers of magnetic changes is to
extend the large number we already possess of mean determinations of
solardiurnal variations, and to add fresh numerical or quantitative values
of the deviations from these means, produced by the causes we class as
irregular.
2 . This appears to me to be persevering in a path we have been travel
ling for forty years Avithout reaching, or even seeing the way, to any
physical explanation of the phenomena.
3. There are about seventyfive points on the globe at which the
diurnal variation, including disturbances, has been determined by eye
observations, hourly or bihourly, with more or less completeness and
precision. The irregular, or nonsolardiurnal, effects have as yet been
eliminated for a few only (ten or twelve) of these points, but this number
has proved sufficient to bring out pretty clearly certain general laws to
which no key has yet been found.
4. Unless it can be shown, that a multiplication of numerical data
promises to bring us to a conclusion, I am inclined to think that the
laborious compilation of more data of the same kind by measurements
from photographic registers, which are less precise than the old eye
observations, is rather a misdirection of energy, unless indeed at stations
widely remote from any others, and where new facts may be expected
(see, for example, the very anomalous diurnal curve at Reikiavik, Iceland,
'Athabasca volume,' p. 297). The recent circumpolar stations would
have come into this category if they had used selfrecording instruments.
5. Airy and Sabine have both taken ± 3'"3 of declination as the
measure of a disturbed observation at Greenwich and Kew respectively.'
If it is true, as remarked by Professor Balfour Stewart (par. 5), that the
precise measure is of no great consequence, is it worth while to spend
much time over making out a new value independently for any part of
Great Britain ?
6. The arbitrary nature of Sabine's mode of treatment of observations
is to me a strong objection to the continuance of it.
For example, he threw out as disturbed all the observations at Point
Barrow which deviated 22'87 from the normal,^ and at Fort Carlton ^ all
which deviated 6'0. But I think I have sufficiently shown that in high
latitudes in America the mean value of disturbance is about three times
' Phil. Trans. 18601863.  Phil. Trans. 1S57. ^ St. Helena, vol. ii.
72 EEPOET 1880,
as great in the early morning hours as it is in the afternoon. Conse
quently we must either disregard a great many observations by day, which
are really disturbed, or include a great many by night, which are not,
unless we say that instability is the same thing as disturbance.
7. What, then, is to be done with the photographic registers ? How
can they be compared unless by ordinates, measured at points agreed
upon, such as the Gottingen hours ?
I reply (1) that I think that each observer should minutely scan his own
records, and note the time, direction, and amount of movements. (2) That
the efiPorts of magneticians should be addressed to the cheap pulolication
and prompt interchange of the registers of each week, reproduced and
reduced by photography to a uniform scale, say 15mm. to 1 hour, with a
view to the discovery of periodically recurring movements of whatever
nature ; of movements apparently local, or not generally traceable ; and
of movements which were general, in one or more elements, over a large
part of the earth's surface.
It hardly meets this suggestion to say that we have hundreds of
projections of disturbances already, and that nothing has come of it. It
is true ; but these projections are scattered through many volumes, are
upon all sorts of scales, and are rarely comparative.
8. The student having by his eye comparison grasped the general
features of the movements constituting disturbance at some particular
epoch, or presenting an exceptional character, the need of measurements
would arise, and if a reference to the mean of the day or the mean of n
days or of the calendar month is necessary, such mean can be ascertained.
I am not sure that it often will be, and I doubt whether our adherence to
the calendar month is rational. Why should movements on May 31 be
referred to the mean for May rather than the mean for June ? The more
accurate, though more laborious, plan would be to refer them to the mean
for May 31 ± 10 days.
9. The end of the needle which points to the equatorial region has in
every locality a mean position in relation to the meridian from which it
is continually deviating, and to which it always returns. It appears to
me open to question whether the relation of the direction of the move
ment to the absolute declination, as increasing it or diminishing it, has
much to do with the question. At least it seems to assume that the
normal position is due to the same physical causes as produce the devia
tions, and therefore I think that the deviations, whether of the polar or
equatorial end, should be simply noted as east or west without regard to
sign. In the southern hemisphere it is the equatorial end that we observe.
Eegions where the north end is actually directed to the south, as at Port
Kennedy and the Alert's winter quarters (18756), will require negative
signs.
10. It seems probable (1) that the mean position of the needle above
referred to is always perpendicular to the direction of electric currents in
the crust of the earth, or the atmosphere, or both, originating in a thermo
electric action of the sun on the meridian, and propagated north and south
from the ecliptic ; (2) that the position of the meridian of the place, in
reference to the sun, determines the direction of the mean deviation of
the needle from its normal position or the mean solardiurnal movement,
and that the amount is determined by a balance of forces still to be clearly
defined. The amount is known at a sufficient number of stations to test
any law laid down.
ON COMPARING AND REDUCING MAGNETIC OBSERVATIONS. 1 3
11. Ifc appears that so long as the sun is above the horizon of the place,
there is comparatively little disturbance. In other words, the hours most
habitually disturbed are before sunrise and after sunset. It is true that
disturbances, once originated, display themselves simultaneously at dis
tant localities, irrespective of the hours of the day ; but the above seems
to give probability to a conjecture that they originate in that hemisphere
from which the sun is absent, and on those meridians which are at the
time in the condition of greatest mean disturbance.
12. Of known physical causes, the influence of sudden internal per
turbations analogous to those which become perceptible to our senses, as
earthquakes and the like, seems to me the most nearly to meet the
observed facts. They cannot be due to any atmospheric cause. Nor is it
very probable that anything extraterrestrial, such as solar perturbations,
can operate with such vigour and suddenness upon our electric circula
tion. That there is a sympathy or correspondence between seismic dis
turbance and magnetic disturbance has been often shown, but I am not
aware that it has ever been followed up in a comprehensive way.
That this view implies some relation between the internal perturba
tions referred to, and the position of the part of the globe in which they
originate in respect to the sun, as being in the hemisphere turned away
from him, appears to follow, but I do not see any absurdity in such a
supposition.
13. Since continuous automatic registration affords a means of tracing
the coi'respondence of either shorttime or longtime movements with
other observed phenomena, seismic movements, solar outbursts, auroral
discharges, and atmospheric changes, for example such as no multiplication
of eyeobservations can do, this appears to me the first use to put it to.
Forty years of eyeobservation have added enormously to our store of
facts, but brought us little if anything nearer a theory. Is it not time to
try some other line of investigation ?
14. With respect to the behaviour of the horizontal component during
disturbances, depending as it does upon two variables, the dip and total
force, it is rather unsatisfactory, but we have good and extensive data,
and whatever principle of measurement or solution is applied to, the
declination, must, I apprehend, be extended to this element.
15. With respect to the vertical component I doubt whether the
available data are as yet comparable in precision with those of the other
two elements. I saw, however, some admirable curves at Toronto, pro
duced by Professor Carpmael's new instrument (I feel doubtful now
whether they were curves of A Y or A0), which had all the character and
freedom of those of the horizontal force, and when these have been worked
np and discussed we shall know a good deal more about the influence of
disturbances in increasing or diminishing the dip and total force.
III. By Professor Schuster, F.R.S.
I should like to submit to the Committee a few points to which their
attention, in my opinion, might with advantage be directed.
It is now nearly fifty years since Gauss applied the method of expan
sion in spherical harmonics to the elements of terrestrial magnetism. He
considered his results only as preliminary, on account of the incomplete
ness of the data on which he had to work.
74 EEPORT — 1885.
We possess now so much more information on the mean value of the
terrestrial elements at different places, that, it seems to me, a repetition
of the calculations of Gauss would lead to valuable results. Such a cal
culation would not only be of theoretical importance. For we might in
this way detect many points of interest, as, for instance, where if anywhere
masses of iron are present near the surface of the earth in sufficient
quantity to affect the magnetic elements. At such places we should ex
pect the harmonic analysis to give correct results only if extended to a
large number of terms, so that if we confine ourselves, like Gauss, to four
or five terms only, and find considerable differences between the calculated
and observed values at some part of the earth's surface, we should have
our attention specially directed to that part.
It is only by a reduction such as that of Gauss that we shall be able
to find out where we require further observations, and where a multiplica
tion of observations is unnecessary.
It would be very desirable if we could extend the analysis of spherical
harmonics to the daily variation of the elements and to magnetic dis
turbances generally. But it seems to me that if, as is likely, these changes
are due to electric currents either above or below the earth's surface but
near it, the analysis would have to be carried to a large number of terms
before it would yield satisfactory results. But this, of course, is a matter
which the actual calculation only can settle, and we ought therefore, at
any rate, to make the attempt to apply the method of Gauss to the daily
variation. With our present knowledge of that variation at different
places of the earth's surfaces, there ought to be no difficulty in finding
out whether five or six terms are sufficient to represeut it, taking ac
count, of course, also of those terms which have their origin outside the
earth.
Some observations of Sabine made near the magnetic pole " seem to
point to the fact that part of the diurnal variation is due to a vertical
component of an electric current crossing the earth's surface. Whether
such a vertical component exists can be determined without difficulty, for
we can actually measure it by taking the line integral of magnetic force
at a given time over a closed curve on the earth's surface.
I should like, therefore, to propose to the Committee to find out, in the
first place, what determinations of the magnetic elements ought to be
taken account of in the reductions. In countries where we possess a great
number of accurate data, it would seem only an increase of labour to take
account of all of them. On the other hand, where we possess few
measurements we should in all probability have to use even approximate
determinations. It is a point for the Committee to decide whether we
ought to take the places which are to be included in the calculation spread
as evenly as possible over the earth's surface, or whether a preponderance
should be given to places near the magnetic poles or at other places of
special importance. Also whether the more accui'ate observations ought
to be weighed. Should the Committee approve of these reduction.=5, it
would be well to ask at the next meeting of the Association for a sufficient
grant to engage the assistance of one or two computers.
I should like in conclusion to submit a few observations respecting
the remarks made by Professor Balfour Stewart and Sir Henry Lefroy.
The function of the Committee seems to me to be a double one. In the
' See Encyclopedia Britannica — Terrestrial Magnetism (art. Meteorology).
ON COMPAKING AND EEDUCING MAGNETIC OBSERVATIONS. 75
first place, they are to discuss the best methods of reducing magnetic ob
servations ; but, before these methods can be put into execution, we must
secure that the observations taken at different places are sufficiently
homogeneous to admit of a common treatment. As we have to deal not
with the individual observations, but with numbers which have already
been reduced at the different observatories, it is clearly of importance that
these preliminary reductions should be done everywhere in the same
manner. Professor Stewart's suggestions refer exclusively to this point,
while Sir Henry Lefroy rather discusses the question as to how the measure
ments already in existence can be made to yield information of physical
value, and as they are treating of different matters, there does not seem
to me to be necessarily any real difference of opinion between them.
While agreeing entirely with a great many of the remarks made by Sir
Henry Lefroy, I believe that some common method of reduction like that
proposed by Professor Stewart is necessary before we can gain any know
ledge of magnetical disturbances. With regard to the proposals them
selves, the principal question will always be, whether the different heads
of observatoi'ies can be made to agree on a uniform plan. The exact
nature of the method of reduction is a matter which has to be settled
chiefly by those who have practical experience in magnetic observatories.
The method of rejecting disturbed observations, commented upon by
Sir Henry Lefroy, is, no doubt, open to objection. If it was simply our
object to gain information on the mean value of magnetic elements, no
observation however much disturbed ought to be rejected ; but as soon as
we suspect that the mean value is not the normal value — that is to say,
that disturbances act more frequently in one direction than in another —
we are necessarily driven to adopt some method of rejecting disturbed
observations. The objections raised by Sir Henry Lefroy against the par
ticular method employed by Sabine seem to me to be, however, very
serious, but I can see no difficulty in amending that method so as to
render it free of the difficulty.
IV. Letter from Professor 0. H. Darwin, F.R.S.
Cambridge :
June 10, 1885.
A 'priori I should not have thought of distinguishing between mean
and normal values, but I suppose that it is desirable to do so. It is
obvious that if all the observations for a month are analysed, we get the
mean harmonic constituents. Then if we recompute the values with
these constituents (which may be done with a tide predicter), and sub
tract the hourly values from the observations originally analysed, we get
a series of residuals. Supposing from those residuals we arbitrarily cut
out a certain number which are above some arbitrarily chosen magnitude,
and submit the rest to harmonic analyses, and supposing these presen1>
us with a new series of constituents with pretty constant phases and
amplitudes, then it would seem to me that we should be justified in the
hypothesis that normal and mean are not the same thing. I must suppose
that some process more or less equivalent to this has been carried out.
I do not observe that any proposal is made to submit the monthly
constants derived from harmonic analysis to a further analysis, and thus
to derive the annual, semiannual, and terannual inequalities of the con
76 EEPORT — 1885.
stituents. My meaning is tliat we ought to express the result in sets of
terms of this form.
Aq + A, cos e + A„ cos 2 + . . .1
+ ai sin B + a, sin 2^+ . . . .]^^^ '?
Bo + B, cos + Bo cos 2 e 4 . . . ■) .
+ &i sin a + io 'sin 2 + . . . . / ^^^ ?*
I had some time back a letter from Chambers at Bombay in which he
says that he considers he has detected a lunar inequality. Now, unless
this is certainly incorrect, is it not desirable to submit the quantities to
analysis according to lunar time ? I take it that your proposal as to
spherical harmonic representation is to put the Aq, Aj, A2, aj, ag, &c.,
as constants multiplied by spherical liarmonic functions of the latitude
and longitude of the place of observation, Gauss had, as I fancy, only
considered the mean values in this way, and you are proposing to treat
the diurnal inequality in a similar manner.
If much harmonic analysis is to be done, some form nearly like that
used for tidal reductions would seem to be useful.
The chief complication of those forms consists in the fact that the
tideheights are taken at exact solar hours, whereas we want measure
ments taken also at mean lunar and a number of other kind of hours.
All this is avoided in your case, unless indeed you carry out an analysis
for the alleged lunar influence.
Yours sincerely,
G. H. Darwin.
V. 'Motes on the above Suggestions. By Professor Balfour Stewaet.
The suggestions of the Committee are invited upon the following
points :
1. Do they agree with the suggestion of Dr. Schuster, that it is of
importance to ascertain the solardiurnal variation of the three magnetic
elements at various stations of the earth's surface, with the view of treat
ing these after the method of Gauss ?
2. Assuming that observations made at stations near the magnetic
pole need special treatment, do the Committee think with Sir Henry
Lefroy that even in ordinary localities the method of Sabine is objection
able for obtaining a correct value of the solardiurnal variation ? As a
good many declination observations have been treated by this method it
is of importance to set the question at rest, and the suggestions of .the
Committee are invited as to the best means of doing this.
3. What do the Committee think of the hereinrecorded method of
obtaining the solardiurnal variations in the case of the hoi'izontal and
vertical force instruments ? I may state that a point of immediate
scientific importance arises regarding the V. F. solardiurnal variation,
inasmuch as the observers at Lisbon and Bombay suspect that this, unlike
the diurnal variations of the other two elements, does not vary with the
state of the sun's surface. It would be very desirable to obtain con
clusive evidence of this from other stations.
ON COMPARING AND REDUCING MAGNETIC OBSERVATIONS. 77
VI. Bemarlcs on Magnetic Reductions. By Senhor Capello.
The method of the separation of the disturbances of the readings of
the bifilar and the vertical force, of which I have sent a resume, and the
examples of the calculation of the last year, seems practical enough to me,
although it will give some trouble. It has, however, retained the prin
cipal fault, the arbitrary nature of the quantity which constitutes the
disturbance. To practise this method upon the hourly observations of
the vertical force is not, I think, more difficult than upon the bifilar.
With respect to the verticalforce instrument of this observatory, I do
not find it very inferior to the bifilar, except for some months on two or
three occasions, during which the equilibrium position was not good, for
the curves had shown a jumping motion ; otherwise it has answered
almost as well as the bifilar, notably in the three or four last years,
where the coefficient of temperature is very much reduced by the adop
tion of a contrivance to compensate the effects of temperature.
Our photographs already embrace twentyone complete years. The
meteorological work, and the care connected with the administration of
the observatory and the meteorological stations absorb the greater jiart
of our time. The reductions of the magnetic observations are very much
behind, and it would be difficult to advance simultaneously all the
elements as they should be ; therefore I think that it would be convenient
to establish an agreement upon the work which by preference it is de
sirable to accomplish, and for what period for a general comparison.
With regard to No. 7 of the suggestions of Sir J. H. Lefroy, I am en
tirely of his opinion, and I will add my ideas upon some researches that
I think would throw light upon the causes of the disturbances.
1. In a paper by Messrs. Capello and B. Stewart (' Proc. R. S.,' January
28, 1864;) upon a first comparison of the disturbances at Kew and at
Lisbon, we have recognised that of the little and abrupt disturbances of
three to five minutes' duration (which are called peaks and hollows), and
which are seen simultaneously in the three curves, those of the decli
nation and of the vertical force are in the same direction at Kew and in
the contrary direction at Lisbon ; that is to say, while tho north end of
the declination needle at Lisbon goes towards east the same end of the
verticalforce instrument dips. The contrary happens at Kew, the north
end of the declination needle going towards east, while the same end of
the verticalforce raises itself.
Again, on the other hand, we have also recognised the agreement of
the behaviour of the peaks and hollows of the declination curves at Kew
and at Lisbon. Thus one vertical peak at Lisbon corresponds always to
a hollow at Kew, and vice versa. It would be interesting (1) to extend
this research upon peaks and hollows further ; that is to say, between
more distant observatories, employing the utmost rigour possible in the
timemeasures, in order to recognise if the times of the appearances of
the peaks are absolutely the same, or if there is a sensible difference in
the most distant observatories. (2) Again, we ought to look in some
observatory immediately between Lisbon and Kew in order to see if the
verticalforce peaks correspond sometimes to the peaks, sometimes to
the hollows of the declination.
2. For the study of the disturbances I think it would be necessary
that each observatory furnished with magnetographs should make pro
78 KEPOET — 1885.
jections upon tbe plaue perpendicular to the inclinationneedle, of the
movement during tbe disturbance of tbe dipping pole of sucb a needle
supposed to be suspended without friction by its centre of gravity. ^
This projection ought to be constructed by means of the declination
variations ( A<i) and those of the inclination (At) ; the first being multi
plied by the cosine of the inclination (cos /), in order to its reduction in
the inclination direction.
The readings of the thiee curves being made at the time of the first
meridian, chosen at intervals of 2 m., 3 m., or 5 m., according to the
deoree of precision which is desired, their differences are taken by com
parison with the first reading, and these differences should be reduced
according to the values of the coefBcients. In combining the values of
the movements of the vertical force and of the bifilar, we find by the
known formula (^ At=3in icosiY ^ _ ^ j J the variations of the incli
nation ; these variations are projected upon the chart in vertical directions,
havino' reference to the first reading, and those of the declination in
horizontal directions, employing a convenient scale.
Here is an example: — Four hours of the disturbance of the 1st of
February, 1881, Oh. to 4 h. (time of Pawlowsk) at Kew, and Lisbon
readings being at the intervals of five minutes.
It is noticed that all the movements are reproduced in the two figures.
They are generally at great length, and now and then deformed at Kew
and of different inclination by comparison with the horizontal line.
All the movements at Lisbon and Kew are executed in the manner con
ti'ary to the hands of a watch. The aspect is sooner at Kew.
If Ave make a similar research upon other more distant observatories —
for example, Pawlowsk and Toronto — the same movements are still re
marked ; but some aspects are completely deformed, the movements at
Toronto being executed in the manner of the hands of a watch.
The measurements in these researches have been taken from the
curves of a scheme of a study of Mr. Wild upon the disturbances of
February 1, 1881.
VII. Observations on Magnetic Reductions. By Dr. H. Wild.
As Messrs. Balfour Stewart and Brito Capelloin the ' Suggestions for
the Committee on Magnctical Reductions,' as well as Herr T. P. van der
Stok in the ' Communications of the International Polar Commission,'
No. 109, have clearly shown, there are to be distinguished in the varia
tions of the magnetic elements — 1st, their normal daily periods ; 2nd,
the slow and constant changes which the absolute values of the days'
means of these show ; 3rd, the eventually different daily periods which
• I think that it would be possible to construct a very simple instrument which
could well register b) photography all such disturbances, which would make these
researches less laborious, avoiding all the measures and reductions which are alwaj's
laborious. Let a little needle be suspended conveniently by the centre of gravity,
employing a thread of silk. In one point of this needle let there be a mirror per
pendicular to its magnetic axis. A luminous slit might be made to fall almost
perpendicularly upon the mirror, registering the movement in all the directions of
the needle. In order that these movements should not be confounded and super
posed, the registering cylinder should proceed by jerks from hour to hour, or of tener
according to experience.
ON COMPARINa AND KEDUCINa MAGNETIC OBSERVATIONS. 79
the deviations from the normal daily path show.' In how far we are to
conceive of the two last variations as disturbances must, in my opinion,
be decided by experience.
In any case we require, for the fixing and estimation of these last varia
tions, a distinct starting point, which the normal daily path may present.
It is, therefore, specially important here to establish this normal daily
path of the magnetic elements. Now regarding the method which Sabine
has devised for this, and also used so much, there is, in the first place,
displayed what Lefroy, Weyprecht, and others have made so prominent,
the arbitrary nature of the limits which are assumed for the expulsion of
the so called disturbed data. Among the different proposals which have
been made for a rational fixing to these limits the most worthy of notice
is that of Buys Ballot, in which these limits are to be set where the devia
tions begin to show another period. Van der Stok has distinctly modified
the Sabine method for the discovery of the normal daily path. His
altogether very complicated method suffers, in my opinion, from the same
wide evils as the Sabine method, viz., that it proceeds from the daily
paths, derived, like them, from the sum of all observations without dis
tinction, i.e. including disturbances. Now it is evidently, as Weyprecht
has already shown, impossible out of the so procured data to get rid alto
gether of the influence of the disturbances on the normal daily path, if
these are not quite irregularly distributed over the day, but are all subject
to a certain daily period. Lefroy again, in his working out of observations
at Tort Simpson and Lake Athabasca, has not employed all the data for
the deriving of the first hour's means, but only the days and hours which,
according to him, weie not to be regarded as disturbed, i.e. where the
amplitude of the movements does not go beyond a certain limit. The
fact that the exclusion of these movements is not settled through the
criterion of Buys Ballot on the one hand, as well as the consideration, on
the other, that days with not less amplitude of movement may also be
disturbed, because the disturbed periods might unite with the normal
periods, so as to weaken themselves through interference (which, as we
shall see, is partly the case), prevents the method from being satisfactory.
In the Programme and in the Sittings of the fourth International Polar
Conference in Vienna (April 1884) I have given out and developed a
new method for the derivation of the normal daily path of the magnetic
elements (see ' Communications of the International Polar Commission,'
No. 94, p. 199 ; No. 97, pp. 208, 211 ; No. 98, pp. 254, 255, 257, 258),
■which is supported by the observation that in the magnetograph traces,
even at the epoch of maximum disturbances, in every month are to be
found a number of days in which a quite regular, and also as regards
these days concerned a recurring periodical path is distinctly recognised.
I regard these days as days with undisturbed daily paths, and the
hourly means of all these days as representative of the normal daily path
of the elements concerned in the month in question, according to its
relative as well as to its absolute size. The selection of these normal days
may from the first likewise seem very arbitrary ; in practice, however,
this is not the case, as hardly a doubt can arise as to which days are to
be taken, and besides the result will not be very distinctly different
whether one chooses one or two days more or less, if from the first one
'For the sake of simplicity I have spoken here only of the daily periods ; clearly
for the remaining periods also, which show the variations of the earth's magnetism,
suitable distinctions can be made.
80 REPORT — 1885.
only takes the precaution to eliminate through linear interpolation any
sudden and individual disturbances which in such days at times
show themselves. The differences of all the observed data from the so
obtained values of the normal daily path in each month I regard as
deviations from the normal, eiSected by some disturbing circumstances.
Should, e.g., all these deviations for all hours' values be put in the form
of a table, and should each be distinguished as positive and negative,
either by certain signs or, according to Balfour Stewart, by different
colours, we should recognise at once, from the similarity of the signs and
the nearly similar size of the figures, whether a day was disturbed uni
formly positive and negative, and from the recurrence of the positive
figures at certain hours, and negative in certain other hours on different
days, whether the disturbance points to a new period different from
the normal daily periods. In order to establish these conclusions with
numerical correctness, it is best to group the deviations according to their
extent, separating negative and positive, and then to investigate their
periodicity as Buys Ballot has proposed.
Herr D. Miiller has worked out according to these principles the
jottings of the magnetogi'aph in the Observatory of Pawlowsk for the
period of the International Polar Expedition, August 1882 to August 1883.
His important results have been laid by me befoi'e the Imperial Academy
of Science, May 21 and June 2, 1885, and are at present published
in the ' Repertoriura for Meteorology.' Without entering into the details
of Herr Miiller's results, I only remark that the success of the first
attempt seems to speak well for this method. The course of the contained
normal daily path in the separate months has unexpectedly become regular
for all three elements — declination, horizontal and vertical intensity, and
also for inclination and total intensity. The days' means of the normal
days show proportionally small differences, and only the greater devia
tions have a pronounced different periodicity, which again is different for
the positive and negative. Herr Miiller has therefore only pointed out
the latter as disturbances, and the former as simple oscillations about the
normal path. For two months, October 1882 and March 1883, I have
prepared a compai'ison of Sabine's method for the declination with that
got by Miiller from my method. Here, in the calculation according to
Sabine, + 2 is assumed as the limiting value for the expulsion of dis
turbances ; and these operations for individual hours were repeated as
often as eight times. In spite of this, there is shown by a glance at the
enclosed table that even by the Sabine method the influence of the pre
vaihng positive disturbances late in the forenoon, and of the maximum of
the negative disturbances in the afternoon, could not be eliminated from
the result. I have the intention to get worked out according to this new
method, which, in short, is applicable to all these data, certain traces of
magnetographs in St. Petersburg and later in Pawlowsk from 1870, and
have for this purpose for the whole period chosen the normal days out of
the photograms.
From this came the unexpected result that the number of these at the
time of the minimum of the sun spots is not so much greater than at the
time of the maximum.
ON COMPARING AND REDUCING MAGNETIC OBSERVATIONS.
81
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82 REPOEX — 1885.
VIII. Letter from Sir Frederich Evans to Professor Steivart.
21 Dawson Place, Bayswater, London, W. r
Mai/ 0, 1883.
Dear Professor Balfour Stewart, — I stall be glad to render the
Magnetic Committee all the assistance in my power, but I have been much
out of sorts in my health for some time, and cannot so well undertake
any work requiring much application.
On Tuesday I leave London for a few days, and will take the papers
with me you forwarded on the 6th instant.
Until we see our way more clearly, it is the discussion of the dis
turbances of the Declination needle which appears to me the most im
portant to break ground upon. On a clear insight of the probable laws
at a few selected stations in both hemispheres, a discussion of other
elements might well follow. Too grand a scheme and complicated
methods of research would, I fear, break down. Sabine's methods had, at
least, simplicity to recommend them.
A letter to the above address will reach me.
Yours faithfully,
Fredk. Jno. Evats^s.
IX. Letter from the Astronomer Eoyal to Professor Stewart.
Royal Observatory, Greenwich, London, S.E. :
Jtili/ 8.
Dear Prof. Stewart, — The printed suggestions for the Committee on
Magnetical Reductions arrived at a very busy time, and since then I have
been away fiom home ; hence the delay.
As there is some diflBculty in discussing abstract questions, I think
it would save misunderstanding if you would make your suggestions with
reference to our Magnetical Results for 1883, now in the press, of which
I send you a copy. There are several additions and alterations which I
have introduced in consultation with Mr. Ellis, in order to give as much
information as practicable about the magnetic curves. We now give, in
addition to mean values of the magnetic elements for each day and the
mean diurnal curves for each month, the daily range, i.e., the amplitude
of the diurnal curve for each day, and particulars of all disturbances,
small as well as large (either in the notes or in the plates). Harmonic
analysis also has been applied to the diurnal variations for each month
and for the year.
Now the question is, how far the suggestions of the Committee are
carried out in the results given. As for rejection of disturbances, I am
inclined to agree with Sir Henry Lefroy in his objection to Sabine's
mode of treatment. At Greenwich the practice has been to draw a
pencil curve smoothing down the irregularities of the trace, and to reject as
disturbed those days for which a continuoiis pencil curve, agreeing gene
rally in form with the normal curve, could not be drawn through the trace.
I see no reason to modify this.
Yours very truly,
W. H. M. Chkistie.
ON COMPARING AND KEDUCINa MAGNETIC OBSERVATIONS. 83
X. Letter from George M. Whipple, Esq., to Professor Stewart.
Kew Observatory :
Juli/ 29, 1885.
Dear Prof. Stewart, — I have carefully read the paper you were so
good as to forward to me, ' Suggestions for the Committee on Magnetical
Reductions,' and must confess that I am in most points fully in accord
ance with Sir H. Lefroy.
I would much rather trust to the solution of the various problems of
Terrestrial Magnetism by a farther and more extended series of com
parison of curves than by an extension of numerical processes.
The reduction of the Fort Rae observation shows how enormously
large and frequent the variations may be in some parts of the earth ;
and such being the case, I fail to see how any nseful purpose could be
served by the repetition of the calculations of Gauss.
I think that magneticians should endeavour, if possible, to enter into
communication with geologists and seismologists, and endeavour to trace
out clearly the causes of (what I would term^) superficial variations, pro
bably due, Prof. Schuster says, to electric currents, for localities well
furnished with magnetic obrscrvatories, such as Europe, rather than to
attempt at once to solve the whole problem of distribution throughout the
earth of magnetic matter. I am, yours faithfully,
G. M. Whipple, Superintendent.
P.S. — I enclose also copy of some remarks addressed by Capt. Dawson
and myself to the Vienna Congress on the subject.
Further and additional remarlis on the questions to he submitted to the
Vienna International Polar Conference.
We are of opinion that careful inspection of the observations them
selves will suffice to show the days and hours when the diurnal curve
follows its normal course. From days and hours selected by this inspec
tion, mean curves may be obtained, and nltimately by interpolation a
series of hourly values may be arrived at for every day in the year.
Readings differing from these values by more than a certain separat
ing value should be set aside and discussed as disturbances. It appeal's
to us probable that the principle of determining the mean monthly diurnal
curves for each station from observations selected only on such days as
are shown by evidence of magnetographs elsewhere to have been mag
netically calm, assumes beforehand a uniformity of magnetic conditions
over the globe, and might, therefore, fail at certain stations. A rough
comparison of Port Rae and Kew Observatory results indicates to us that
it is rather more advisable to deal with hours and not with days as a
whole, and that therefore some rule, either Sabine's or Lloyd's, must of
necessity be adopted.
There seems no objection to the application, first, of Lloyd's rule to
throw out disturbances, and then to the subsequent classification of these
disturbances after the method suggested by Wild.
We fail to see as yet any method of introducing possible corrections
for sunspot periodicity into observations made during so short an inter
val of time at stations where no previous observations have been taken ;
and therefore recommend that this disturbing element be omitted entirely
84 REPORT — 1885.
fi'ora the proposed international discussion, and left entirely to specialists
for subsequent treatment.
With regard to the discussion of disturbances, we would suggest that
each expedition should draw up a list of the days, selected according to
Gcittingen time, considered by them a disturbed day, and then from a
comparison of such lists the Conference should decide on what days
should be selected for particular discussion in addition to the term days.
Question 3. — Dr. Wild's suggestion as to plotting the curves is so
very convenient that we have already adopted it in making preliminary
curves of the Fort Rae observations. It will be necessary in addition,
however, to decide upon the scale of abscissa} to be used for the 2U
secoud interval observations on term hours. We suggest the employment
of a scale giving six minutes of abscissaj to each minute of time.
Questions 4 and 5. — The conversion of Gaussian units into those of
the C.G.S. system is so simple that it is unnecessary for the Conference
to disturb the existing historic system. The Kew Observatory has already
for years published their results in both systems. The footgrain system
is rapidly becoming obsolete, most magnetometers now constructed having
metre instead of foot scales.
XI. Letter from General Lefroy to Professor Stewart.
82 Queen's Gate, S.W. :
Jiili/ 15, 1885.
My dear Professor, — I have carefully read, and return herewith, the
papers of Senhor Capello and Dr. Wild. I have difficulty in attaching
a physical idea to the ingenious method of projection proposed by Senhor
Capello. He gives the movement, projected on a plane perpendicular to
the dip of the axis or intersection of the plane of dip and the plane of
declination ; but I do not see how the variations of total force are to be
shown in conjunction with this, or with what physical notions to connect
the resulting curves. The actual realisation of the suspension of a
needle by its centre of gravity without friction in any direction, especi
ally if counterpoised to carry a mirror, would be a great achievement,
b'at, with great respect, I doubt its being possible. Still his comparison
of Lisbon and Pawlowsk is very curious, and strongly conflrms my belief
that, be our stations few or many, the results at all of them must be
brought into one view, by identity of treatment and prompt circulation,
to obtain a clue, and to effect this we want a Bens ex machina.
My file of bulletins of the International Polar Commission does not go
beyond Part 5. I have not seen Herr van der Stok's communication, which
Dr. Wild refers to. It has occurred to rae, following a hint of Lloyd's,'
that the area of movements would be a good measure of the forces pro
ducing them, and that it might be possible by an instrument on the prin
ciple of Amsler's planlmeter to integrate these areas for the whole
twentyfour hours, or any not very small portions of it, in moderate dis
turbances. The extremely active ones would not be easily measurable.
To take cognisance, as has sometimes been done, of those movements
only which coincide with hours of mean time or Gottingen time, appears
to me to forego the special advantages of continuous recoi'd. I agree
with Dr. Wild that there is no difficulty in selecting the normal days at
' Trans. R.I.A., vol. xxii.
ON COMPARING AND REDUCING MAGNETIC OBSERVATIONS. 85
any station, but whether they woulcl be the same at other stations has
not, as far as I know, been ascertained. Lloyd, as you know, worked out
the consequences of adopting every possible value of disturbance test.
Sabine has given two or three values, all purely empirical. If my plan
of areas were practically feasible, it does seem to me free from that ob
jection. Dr. Wild appears to disregard magnitude, and to refer all the
observed data to his normal values, and I think nothing less comprehen
sive will be found satisfactory in the long run. It is gratifying, however,
to find that his results are not widely different from those obtained by
Sabine's method. As Dr. Wild quotes Toronto, I suppose that some
hmited circulation and occasional comparison does go on, but Carpmael
has no staff to keep it up regularly. We all want more hands, which
means more money.
Believe me faithfully yours,
J. H. Lekrot.
XII. Observations, S,c. By Chakles Chambers, F.R.S..
Superintendent, Colaba Observatory, Bombay.
There can be little doubt that the activity displayed during the last
quarter of a century in the record of the phenomena of terrestrial mag
netism was induced mainly by the interesting results to which Sabine
was led in his discussions of the observations of the British, colonial, and
other observatories ; that it was in the hope of extending and completing
such results by wider observation, that men of science in all parts of the
civilised world urged upon their respective Governments the advisability
of establishing magnetical observatories. Few who have studied Sabine's
memoirs — displaying, amongst other remarkable generalisations, the out
lines of a system of the globe in respect of the regular solar diurnal
variations and the variations of these with the season of the year, and
connecting with the sunspot period variations of the range of the regular
diurnal variation of declination and of the aggregate amounts of dis
turbance — will doubt the wisdom of the influence thus brought to bear
on the guardians of the public purse, nor, whatever else may be done, of
the propriety of carrying the work to the legitimate conclusion of extend
ing and completing Sabine's results. To act otherwise, in the absence of
a physical theory to which there is as yet no clue, would be to admit a
change of judgment which there is nothing in the circumstances of the
present day, any more than there was at the time when the work of auto
matic registration was initiated, to justify, and would, moreover, be to
discourage the statesmen who, by the provision of funds, have aided in
the production of records of the crude phenomena, from making farther
sacrifices in that direction : these dignitaries would, in their capacity of
trustees for society, rightly complain that they had been led to expect
systematised knowledge, but had been given instead piles of records of
unused facts, and that the responsibility and expense of preserving these
is scarcely a substitute for the reward they had been dazzled with the
promise of.
2. In my opinion the scientific authorities, on whose advice much
money has been spent in procuring many years' continuous records, are
bound in honour to see that the representations which induced the various
Governments to provide funds are justified by at least a full carrying out
86 REPORT — 1885.
of tlie original purposes as to tlie uses to which the records were to be
applied.
3. The fact is that funds have been expended too exclusively upon
material appHances, and upon agency for working them : the statesman
can understand that his country gets a tangible return when observa,tory
buildings, instruments, operators, records, and reports appear before him
as a result of the grants that he makes ; but it is for the man of science,
the original adviser, to make him understand that these are very delusive
results unless supplemented by appropriate measurement, computation,
and discussion.
4. And this is the more important inasmuch as the cost of utilising
the records, even up to the point suggested by Sabine's examples, will
at least equal the amount that has been expended in their production.
It is indispensable that inexpensive measuring, copying, and computing
power should be used, under skilled direction, on a large scale ; and here
it is that the main part of the cost arises. It would be simple waste of
superior energy to set a cultivated physicist to the appalling task of per
forming the simple but multitudinous series of operations thataie involved
in any adequate treatment of the observations ; and it is to the insufficiency
of suitable agency in the working power of existing observatories that is
probably to be attributed the fact that so little has yet been done in the
way of independent reduction and discussion of the records of the auto
matic magnetic instruments. That the work before us is laborious and
costly is, however, no argument against the undertaking of it if we have
reason to believe that an adequate return will be obtained ; and a more
costly process is to be preferred to a less costly one if the quality of the
results that are the outcome of it is higher in a corresponding degree.
5. I cannot but think that the wonderful progress made during the
last century in the experimental sciences is apt to make us unduly im
patient of the necessarily slower progress of the observational sciences.
If astronomy had, during the progress of observation, to have its period
of phenomenal generalisation — its Ptolemy, its Copernicus, its Kepler—
before light as to the mode of physical causation dawned upon its
Newton, is it much to be wondered at that a much more complicated
science, as terrestrial magnetism undoubtedly is, should have to pass
through its period of discoveiy of general phenomenal relations — relations
which the physical theory will ultimately have to explain — before the
conditions essential to the conception of a general theory can be laid
down ?
6. It will be seen that whilst I have no faith in the flights of genius
that would look at the crude facts as nature presents them to us, and
from such comj^lex data devise a theory to unravel the complexity, I have
the greatest confidence in appropriate methods of analysation as leading
to relatively simple jDhenomenal generalisations, and thence, inevitably in
the long run, to the desired physical theory. The first step to be taken
should, I think, be to collect together all accessible results that have
already been worked out and published of the nature of —
(1) The regular solardiurnal variations;
(2) The disturbance variations — diurnal, annual, and secular ; and
(3) The lunardiurnal variations ;
and to convert the expression of them for each of the elements, declination,
horizontal force, and vertical force, as far as available, into metregramme
second or C.G.S. units of force. If not already done, the averages of
ON COMPABINa AND EEDUCINa MAGNETIC OBSERVATIONS. 87
{1) should be calculated for each month from the separate results of all
the years that are available, and curves be constructed to represent these
average monthly variations according to timescales and forcescales which
would be marked on the curveforms. It would be convenient that the
curves should appear, for any one station, in a row, beginning with
January, on a long narrow slip of thick paper, so that the sets of curves
for any one station might be placed close under those of any other
station for easy comparison. For preservation, the slips of paper would
be kept in a portfolio, not bound into a book. Curves on a less elaborate
scale, as would be suggested by the meagreness (or fulness) of the
materials collected, might similarly be constructed on slips to represent
the variations (2) and (3). Such series of curves, to the extent to which
data for them would be found easily accessible, would, I imagine, con
stitute a conclusive answer to those who doubt the utility of extending
investigation in the same direction ; but, taking continuity of change of
character of the variations in passing from place to place as a criterion
of the value and importance of the results obtained, they would also
serve the further purpose of suggesting whether and where Sabine's
methods are exact enough, or to what extent the application of even more
laborious processes of reduction would be justified. These curves should
be lithographed on thick slips of paper, and distributed amongst the
directors of observatories and other students of terrestrial magnetism ;
and, as little in the shape of description or comment need accompany
them, the originals could be produced by agency of an order that should
be readily obtainable, and that would require but little supervision, from
some specialist member of the Committee.
The curves might, with advantage, be accompanied by a table of the
absolute values of the elements declination, horizontal foi'ce, and vertical
force for each station ; and also by tables of ranges of the solardiurnal
variations of each element on the average of each full year.
7. It has been well established by Broun and myself that the socalled
lunardiurnal A^ariation is a function both of the season of the year and
of the age of the moon, and there is reason for believing that the bulk of
the phenomena is really a part of the regular solardiurnal variation, a
part that reverses its character four times in the course of the lunation.
Now the adoption, by Sabine's process, of a uniform solardiurnal
variation for the whole of a calendar month, whilst perhaps accurate
enough for the determination of the general character of the disturbance
laws, leaves much to be desired when the object we are in quest of is a
minute variation which has, in the case of the declination, a less range
than a single minute of arc, and which is subject to variation of character
with change of season. Here we require that a mean solardiurnal
variation should be calculated for each individual day, in order that the
elimination of mean solar effect should be nearly complete ; and knowing
that either a part of the solardiurnal variation, or the bulk of the lunar
diurnal variation, runs through a cycle of change in a lunation, the best
period for which to calculate the daily means is a mean lunation, or the
nearest odd number of mean solar days to a mean lunation — that is to say,
twentynine days. The importance of this period should be kept in view
from the first, whether or not there is any immediate purpose of investi
gating the lanardiurnal variations, and my present object is not so much
to advocate the inclusion of such investigations in the first general
scheme of operations as to explain why the period of twentynine days
88 REPORT — 1885.
enters into modiScations that I would suggest of tlie procedure proposed
by Dr. Balfour Stewart in dealing witli the horizontal force tabulations,
Taut whicb modified process should, I think, be applied also to the de
clination tabulations.
It is not a general rule that the hours at which the bulk of disturb
ance occurs are the same for both the elements declination and hori
zontal force ; and hence — thougb it is liighlj probable that distuibance
of some degree in one element occurs on the same day as disturbance of
another degree in the other — we cannot with safety allot the disturbances
to identical hours.
8. First, I would substitute for Sabine's classification of disturbances
as 'larger' and 'smaller,' a division into tho.se that ai'e without the
limits set by the normal ± the separating value, and those that are
within those limits ; and instead of rejecting disturbed observations I
would, at such step of Sabine's process for separating the larger dis
turbances, replace each disturbed entry by the same number minus the
disturbance without the limits — as apparent at that stage. The dis
turbances without the limits would be separated and the laws of their
variations determined by the methods that Sabine applied to his larger
disturbances, but the disturbances within the limits would remain in
volved with the regular variations until a late stage of the investigations.
9. Secondly, as regards jirogressive change in the readings, both of
the declination and horizontal force instruments, it would, I think, gene
rally suffice to treat that change as uniform during the course of a month.
Having entered the hourly tabulations for a given month on a table
(A call it) having the hours marked at the top of the columns and the
days of the month in the first or lefthand column, and having taken
daily means, I M'ould take the mean of the first fifteen of those daily
means and the last fifteen of the preceding nionth's table A as the mean
number for the beginning of the month ; and similarly the mean number
for the end of the month would be the mean of the last fifteen daily means
of that month and the first fifteen of the next following month. Change
at the uniform rate indicated by the mean numbers ' for the beginning
and end of the month I would eliminate from the original hourly tabula
tions of table A, and enter the new number on a new table (B), to which
I would proceed to apply Sabine's (modified) process. This would lead
to a general knowledge of the regular solardiurnal variations for each
month, and of the laws of the disturbance variations ; and here a rest
ingplace might be found if it were desired to compare results from
different stations before proceeding with more elaborate reductions.
10. To proceed, however, I would next, having obtained the amounts
of disturbance without the limits, eliminate these amounts from the re
spective disturbed observations of table A, calling the table thus altered
(A'), and this table should form the basis of discussion in respect of the
regular solardiurnal variations for each day, the lunardiurnal variations,
and the laws of variation of disturbances within the limits.
From table (A'), and the corresponding table of the preceding and
following months, I would construct another similar table (C),each entry
in which would be the 29day mean of the numbers for the same hour
' The effects of disturbances without the limits on the daily means I would take
to be sufficiently indicated by the departures of those means from corresponding
daily means, as calculated from the mean numbers for the beginning and end of the
month, with a uniform rate of change from one to the other.
ON COMPARING AND REDUCING MAGNETIC OBSERVATIONS. 89
in table (A'), viz., of the numbers for the day of the entry and the four
teen preceding and fourteen following days. The numbers of table C
for all the hours of a given day we may take to represent very approxi
mately the mean solardiurnal variation — flus a constant — for that day,
the average extending over the lunation of which that day is the middle
day. They will be affected by progressive change of the values of the
tabulations, and by disturbance within the limits.
11. Lastly, the excesses of the numbers of table (A') over the corre
sponding numbers in table C, fJus a constant round number,^ should be
entered on a fourth table (D). The numbers of this table, which will be
affected only by that part of the solai'diurnal variation which goes
through a cycle of change in a lunation, and by disturbance within the
limits, we may proceed to arrange in new tables with reference to the
moon's age and the season (or month) of the year,^ and so determine
the character of the variations which the lunisolardiurnal variation is
subject to. Having done this, a further elimination will put us in pos
session of residual numbers, the variation of which must be attributed
solely to disturbances within the limits, and may be studied and the
numbers be manipulated accordingly.
12. I agree with Dr. Balfour Stewart that the time has not yet
arrived for laying down rules for the treatment of the vertical force
tabulations.
XIII. Letter frovi the Eev. Professor S. J. Ferry, F.B.S.
Sej)temhcr 8, 1885.
Dear Dr. Schuster, — I have read over the Report Dr. Stewart kindly
forwarded, and I cannot help thinking that our first step should be to
collect the results already obtained for the Daily Range of the Declina
tion, reduce the means already worked out to a common scale, and then
distribute the whole in a tabular and in a graphical form. Much might
be learnt from seeing these results in a collective form, and we could then
better judge how far processes more laborious than those of Sir Edward
Sabine are like to repay the labour.
If all observations are made use of in deducing the Daily Mean Ran^e
the Disturbance period will certainly interfere with the Solar Diurnal
Range, and if we pick out quiet curves in which the Daily Range is well
marked, we are very liable to give undue weight to variations in the
Daily Range which are independent of ordinary disturbances.
Yours very truly,
S. J. Perry.
' The constant round number is added to avoid the inconvenience of having tO'
deal afterwards vf ith jwsitive and negative numbers.
 If a separate table be allotted to each day of the moon's age, the resulting
mean variations will be practically the same whether the hours refer to the solar or
the lunar day ; and as the numbers available are for the exact hours of the solar day, it
is convenient to let the arrangement of the table be for the solar day rather than for
the lunar day.
90 EEPOET — 1885.
Report of the Committee, consisting of Professor Crum Brown
(Secretary), j\Ir. jNIilxe Home, Mr. John Murray, and INIr.
BucHAN, appointed for the purpose of cooperating with the
Scottish Meteorological Society in making Meteorological Obser
vations on Ben Kevis.
Dl'Ring tlie past twelve montlas the observatious on Ben Nevis have
been made every honr, by night as well as by day. This remarkable
continuity in the observations, conducted under such great difficulties, is
due to the enthusiasm and undaunted devotion to the work evinced by
Mr. Omond and his assistants, and to the completion of the Observatory
building last summer with its tower, which admits of a ready egress
from the Observatory when the doors are blocked with rapidly accuma
lating snowdrifts, except during those rare occasions, of which the winter
months of 188485 afforded only one example, in the great storm of
February, when from 6 p.m. of the 21st to 8 a.m. of the 22nd no light
could be carried in a lantein outside to the instruments. This inter
ruption refei's only to the observations of the temperature of the air.
During the year the most notable additions made to the observations
refer to the I'ainfall and the wind. The actual precipitation — rain, sleet,
snow, or hail — has been collected with raingauges specially designed for
the purpose, and measured with the greatest care every hour since
June 24, 1884, with, it is believed, a very close approximation to the
truth ; and the hourly results for each month have been calculated.
In the end of October the anemometers designed by Professor
Chrystal for the Observatory, to register continuously the velocity and
direction of the wind, were added to the observing instruments. Unfor
tunately, however, in tlie colder months of the year the deposition of
icecrystals, which Mr, Omond has described in a recent paper, renders
all anemometei's quite useless, except at rare intervals. During the
seven months from November 1, 1884, to May 31, 1885, there was only a
mean of thirty days in which the anemometer Avas in working order.
During these days the greatest velocity was on the night of April 2425,
w^hen for twelve hours the mean velocity was seventyfour miles, rising
one hour to eightyone miles.
Estimations of windforce have continued to be made every hour
during the year, and the results show, as in the previous year, that the
wind is above the mean daily force during the night and below it during
the day. The maximum occurred from 2 to 3 a.m. and the minimum
from 2 to 3 p.m., the difference between the extremes being between two
and three miles an hour. The means of the observations made since the
Observatory was opened show that the same relation holds good during
each of the four seasons. These peculiarities in the diurnal variation in
the velocity of the wind on Ben Nevis are of the greatest importance,
especially in view of similar curves obtained at other highlevel obser
vatories situated on mountain peaks, and by Mr. Archibald Douglas from
his balloon observations and experiments, and their bearing on atmo
spheric movements.
During July 1885 the anemometers have been continuously at work,
and there are now before us a month's complete hourly records of
recorded velocities and estimated windforce. The curves drawn from
ON METEOROLOGICAL OBSERVATIONS ON BEN NEVIS. 91
the results of these two methods are closely congruent. This double set
of observations supply the data for a more exact conversion of the
estimations of windforce, according to Beaufort's scale, into their equiva
lents in miles. A large number of similar observations made on boaid
the Challenge! also form a valuable contribution to this inquiry. So
far as the observations go, they appear to indicate that the equivalents in
miles usually given for the higher numbers of Beaufort's scale are too
small. From 8 to 9 a.m. of August 9 the anemometer registered
86 miles, and during this hour the estimated force was from 8 to 9
of the scale. The equivalent in miles for this force, provisionally
adopted by the Meteorological Council, is from 48 to 56 miles. What is
the number of miles when an estimated force of 10 or 11, which has
been not unfrequently recorded during the colder months of the year, is
reached and maintained for some time remains to be seen. Instances
will in all probability occur during the autumn before the icedeposits of
the wind practically seal up the anemometer for the winter months.
The mean temperature for the year ending May 1885 was 30°G, or
0°'3 below the calculated normal temperature given in last year's Report.
The tempei'atures for the same period for stations in the more immediate
neighbourhood were from 0°3 to O''^ below their normals, being thus
identical with the deviation from the normal at the Observatory. The
extremes of temperature for the year were GO°'l at 2 p.ji. August 9, and
11°T at midnight and 1 A.M. February 16, thus giving a range of 49°0.
The coldest week yet experienced was the week ending February 21, the
mean of which was lG''2. In this week the lowest temperature for the
year occurred, and the humidity fell to 22. Great dryness associated
with great cold scarcely ever occurs in the weather records of the Ben,
and in this case the exceptionally cold dry weather terminated with the
great storm of the 21st and 22nd February already referred to.
From the observations of the maximum and minimum thermometers
the mean daily range of temperature is — in winter, 6°'8 ; spring, 6°'4 ;
summer, 7°'l ; and autumn, 6°6 — there being thus little variation with
season. From the dry bulb, there is only 0°'7 between the mean coldest
and mean warmest hour of the day in winter, but in summer the diffe
rence is 3°'0. It follows that in all seasons, but particularly in winter,
the changes of temperature which occur are only in a subordinate degree
due to the direct influence of the sun, but are chiefly caused by the
passage of cyclones and anticyclones over the Observatory. Indeed, it
may be regarded that, in the stormy months of winter, the Ben Nevis
observations present the cyclonic and anticyclonic changes of tempera
ture in their simple conditions, uninfluenced by the heat of the sun.
Lower relative humidities were observed than during the previous
year. On January 20, the mean of the twentyfour hours gave the very
low mean humidity of 32. On the 15th of the same month, at 5 a.m., the
dry bulb was 20°9 and the wet 16°2, which from Glaisher's tables indi
cates a dewpoint at — 16°2 and a humidity of 19, being respectively the
lowest yet noted on the top of Ben ISTevis. The lowest temperature ever
observed anywhere in the British Islands was — 16°0, at Springwood
Park, near Kelso, in December, 1879, which closely agrees with the lowest
dewpoint on Ben Nevis. As regards atmospheric pressure, it is only in
winter that the afternoon minimum falls below the mean daily pressure ;
in summer this daily minimum is 0007 inch above the daily mean. On
the top of Ben Nevis, atmospheric pressure of the three seasons, spring,
92 EEPORT — 1885.
summer, and autumn, is above tlie daily mean for fifteen hours, from 10 A.M.
to midnight, and below it for nine hours, from 1 to 9 A.M. In June, when
the sun's heat is most powerful, the afternoon minimum is the least
pronounced, and the diurnal curve of pressure tends towards a single
maximum and minimum, similar to what occurs in the same months over
the open sea in the higher latitudes. Except in midwinter these seasonal
peculiarities of the pressure are seen in the results of each month's obser
vations, and the regularity in the changes from month to month, in the
times of occuirence of the four phases of the pressure, is very striking.
The sunshinerecorder shows 461' hours of suushine for the twelve
months, which is about 11 per cent, of the possible sunshine. As regards
the partition of the sunshine through the hours of the day, the most note
worthy circumstance is that daring spring, summer, and autumn the
amount is very considerably greater before noon than after it. As com
pared with the afternoon, the sunshine of the forenoon is 43 per cent,
greater in spring, 60 in summer, and 33 in autumn, whereas in winter the
amounts are nearly equal. During summer the maximum sunshine occurs
from G to 9 a.m. This diminution in suushine later in the day is no doubt
caused by the ascending aerial currents which rise from the heated sides
of the mountain during the warm hours of the day, and the condensation
of the aqueous vapour into cloud which is the consequence.
Very heavy rainfalls are of frequent occurrence on Ben Nevis. Of
single hours the largest was 1'302 inch, from noon to 1 p.m. of December
10, 1884. The largest daily fall was 4'264< inches, on December 10,
1884, a fall all but equalled by that of October 25, which was 4231
inches. A fall of at least one inch occurs, on the average, one day in
seven. Combining all the rainfall observations made since June, 1881,
the following are the averages ; those from July to September being for
four j^ears, June and October for three years, and November to May
one year only.
inches inches
January . . . 733 May .... 837
February . . 1094 June. . . . 880
March . . . 1289 Juh .... 1070
April . . . 485 August . . . 1124
inches
September . . 944
October . . 110&
November . . 1930
December . . 2520
Year, 14614 inches.
There can be little doubt that the Ben Nevis Observatory has the
largest rainfall of any place in Scotland at which a raingauge has hitherto
been observed.
The observations at Fort William by Mr. Livingston, consisting of
eye observations six times a day, and continuous recoi'ds of the atmo
spheric pressure and temperature by a barograph and thermograph,
have been regularly carried on during the year. It is not possible to
overestimate the value of these sealevel observations at Fort William, in
their relations to the observations made on the top of Ben Nevis, it being
from these relations that the Ben Nevis observations have their supreme
importance in discussing the great problem of the weather changes of
Northwestern Europe. This inquiry is now being carried on under the
superintendence of the Directors of the Observatory.
ON THE RATE OF INCREASE OF UNDERGROUND TEMPERATURE. 93
Seventeenth Report of the Covimittee, consisting of Professor
Everett, Professor Sir W. Thomson, INIr. Gr. J. Symoxs, Sir A. C.
Kamsay, Dr. A. GtEIKIE, JMr. J. Gtlaisher, Mr. Pengelly, Pro
fessor Edward Hull, Professor Prestwich, Dr. C. Le Neve
Foster, Professor A. S. Hersciiel, Professor Gr. A. Lebour, Mr.
Galloway, ]Mr. Joseph Dickinson, Mr. G. F. Deacon, Mr. E.
Wethered, and Mr. A. Strahan, appointed for the purpose of
investigating the Rate of Increase of Underground Temperature
dowmvards in various Localities of Dry Land and under
Water. Drawn up by Professor Everett (Secretary).
The present Report is for the two years wbicli have elapsed since the
summer of 1883.
Observations have been taken in a deep bore at Richmond, Surrey,
by Mr. Collett Homersbam, M.Inst. C.E., F.G.S. It is on the premises of
the Richmond Vestry Waterworks, on the right bank of the Thames,
and about 33 yards from high water mark. The surface is 17 feet above
Ordnance datum.
The upper part consists of a well 253 feet deep, with an internal
diameter of 7 feet at top and 5 feet at bottom, which was sunk in 187G
for the purpose of supplying water to the town of Richmond, and carried
down to the chalk. From the bottom of the well a 24inch borehole
was sunk to the total depth of 434 feet, thus penetrating 181 feet into
the chalk. This portion of the work was completed in 1877. Above
the chalk were tertiaries, consisting of 160 feet of London clay, 60 feet
of the Woolwich and Reading beds, and some underlying sands. TJie
water yielded at this stage was about 160 gallons a minute, and when
not depressed by pumping was able to rise 4 or 5 feet above the surface.
Its ordinary level, owing to pumping, was about 130 feet lower.
In 1881 the Richmond Vestry determined to carry the borehole to a
much greater depth, and the deepening has been executed under the
direction of Mr. Homersham's father, who is consulting ensineer to the
Vestry.
The existing borehole was first enlarged and straightened, to enable
a line of castiron pipes, with an internal diameter of 16^ inches, having
the lower end driven watertight into the chalic at a depth of 438 feet,
to be carried up to the surface. The annular space surrounding this ])ipe
served to furnish an uncontaminated supply of water to the town during
the deepening.
Tlie total thickness of the chalk was 671 feet. Below this was the
upper greensand, 16 feet thick ; then the gault clay, 201^ feet thick ;
then 10 feet of a sandy rock, and a thin layer of phosphatic nodules.
Down to this point the new boring had yielded no water. Then followed
a bed 87^ feet thick, consisting mainly of hard oolitic limestone. Two
small springs of water were met with in this bed at the depths of 1,203
and 1,210 feet, the yield at the surface being 1^ gallons a minute, with
power to rise in a tube and overflow 49 feet above the ground. A partial
analysis of this limestone rock showed it to contain 24 per cent, of
94 REPORT — 1885.
sulphide of iron in the form of pyrites. At the depth of 1,239 feet this
limestone rock ended, and hard red sandstone was found, alternating
with beds of variegated sandy marl or clay. After the depth of 1,253
feet had been attained, the yield of water steadily increased as the boring
was deepened, the overflow at the surface being 2 gallons a minute at
1,254 feet, 8 gallons at 1,363 feet, and 11 gallons at 1,387 feet. It rose
to the top of a tube carried 49 feet above the surface, and overflowed ;
and a piessuregauge showed that it had power to rise 126 feet above
the surface.
The diameter of the bore was 16^ inches in the chalk, 13^ inches in
the gault, llj inches in the oolitic limestone, and at the depth of 1,334 feet
it was reduced to a little under 9 inches. At 1,337 feet the method of
boring was changed, and instead of an annular arrangement of steel
cutters, a rotary diamond rockboring machine was employed. The bore
hole, with a diameter of 85 inches, was thus carried down to 1,367^ feet,
at which depth, lining tubes having to be inserted, the diameter was re
duced to 7j inches, and this size was continued to 1,447 feet, at which
depth the boring was stopped.
The borehole was lined with strong iron tubes down to the depth of
1,364 feet ; and those portions of the tubes that are in proximity to the
depths where water was struck were drilled with holes to admit the
water into them. Three observations of temperature were taken at the
depth of 1,337 feet, during the interval between the removal of the steel
borers and the erection of the diamond boringmachine. The borehole
was full of water, which was overflowing at the rate of from three to four
gallons a minute. The thermometer employed was an inverted Negretti
maximum, supplied by the secretary. In each case the temperature re
corded was 75^° F. In the first observation, March 25, 1884, the ther
mometer was left for an hour and a quarter at the bottom of the borehole,
and three weeks had elapsed since the water was disturbed by boring.
The second observation was taken on March 31, when the thermometer
was 5i hours at the bottom. In the third observation special precau
tions were taken to prevent convection. The thermometer was fixed
inside a wroiightiron tube, 5 feet long, open at bottom. The thermo
meter was near the lower end of the tube, and was suspended from a
watertight wooden plug, tightly driven into the tube. There was a
space of several inches between the plug and the thermometer, and this
part of the tube was pierced with numerous holes to allow the escape of
any cold water which might be carried down by the tube. The tube was
one of a series of hollow boring rods used in working the diamond drill
machine. By means of these it was lowered very slowly, to avoid dis
turbance of the water as much as possible ; and the tube containing the
thermometer was gradually worked through the sand at the bottom of
the borehole. The lowering occupied five hours, and was completed at
noon on Saturday, June 7.
Cement, mixed with sugar, for the purpose of slow setting, was imme
diately lowered on to the surface of the sand, and above this a mixture of
cement and sand, making a total thickness of 3 or 4 feet of cement
plugoing. The thermometer was left in its place for three full days, the
operation of raising being commenced at noon of Tuesday, June 10, and
completed at 5 p.m. The thermometer again registered 75^° F., exactly
the same as in the two previous observations which were taken without
plugging. It would therefore appear that the steady upflow of water in
ON THE EATE OF INCEEASE OF UNDEEGEOUJJD TEMPEEATUEE. 95
the lower part of the bore prevents any downward convection of colder
water from above.
The boring has since been carried to the depth of 1,447 feet, with a
diameter reduced to 7^ inches, and Mr. Homersham made preparations
for a final observation at the bottom with a plug consisting of a thick
indiarubber disc covered with cement and saud ; but the vestry declined
to incur the responsibility of having the rods lowered again for this
purpose ; and as some pieces of broken liningtube had fallen in, there
would have been serious risk of jamming. Mr. Homersham accordingly
contented himself with lowering the thermometer to the bottom without
plugging. It remained down for six days (Febrnary 3 to 9, 1885), and
gave a reading of 76^° F. The water overflowing at the surface had a
tempeiature of 59° F.
To deduce the mean rate of increase downwards, we shall assume a
surface temperature of 50°. This gives for the first 1,337 feet an increase
of 251°, which is at the rate of 1° F. in 624 feet, and for the whole
1,447 feet an increase of 26J°, which is at the rate of 1° F. in 54'1 feet.
These results agree well with the Kentish Town well, where Mr. Symons
found in 1,100 feet an average increase of 1° in 55 feet.
]Mr. Homersham carried on a lengthened correspondence with the
secretary as to the best manner of taking the observations, and the
method devised by him as above described will famish a useful model for
future observers.
Thanks are also due to the Richmond Vestry for permission to
observe, and to the contractors, Messrs. Docwra, for the loan of their
apparatus.
Mr. Galloway (member of the Committee) has furnished observations
taken daring the sinking of a shaft to the depth of 1,272 feet in or near
the Aberdare valley, Glamorganshire. The name of the place is Cwm
pennar, and the position of the shaft is on the slope on the east side
of the valley, near the summit of the hill which separates it from the
Merthyr valley. The mouth of the shaft is about 800 feet above sea
level.
Observations were taken at four different depths, 546 feet, 780 feet,
1,020 feet, and 1,272 feet, the thermometer being in each case inserted,
and left for twentyfour hours, in a hole bored to the depth of 30 inches,
at a distance not exceeding 2Jy yards from the bottom of the shaft for the
time being. About eight hours elapsed between the completion of the
hole and the insertion of the thermometer. The strata consist mainly
of shales and sandstone, with a dip of 1 in 12, and the flow of water into
the shaft was about 250 gallons per hour.
The first of the four observations was taken in the fireclay under the
Abergorkie vein ; the second in strong * clift ' (a local name for arena
ceous shale) in disturbed ground ; the third in bastard fireclay under a
small rider of coal previously unknown ; the fourth in ' cHft ' ground two
yards above the red coal vein, which overlies the 9foot seam at a height
of from 9 to 12 yards. The observations were taken by the manager,
Mr. John Beith, and are as follow :
epth in ft.
546
Temp. Fahr
56°
780
1,020
1,272
69j°
63°
66^°
96
REPORT — 1885.
Comparing consecutive deptlis from 546 feet downwards, we liave the
following increments of temperature : —
3i° in 234 ft., giving 1° for 67 ft.
3i°
■sl°
240
69
— showing a remarkably regular rate of increase. A comparison of the
first and fourth observations gives an increase of 101° in 726 feet, which
is at the rate of 1° F. in 691 feet. As the surface slopes about 1 in 5, and
the pit is near the summit of a ridge, it is probable that in level ground
of similar material the rate would be about 1° F. in 60 feet.
As a check upon this result, we find that this rate of decrease reck
oned upwards from the smallest depth (546 feet) would give a surface
temperature of (56 — 79 =) 48°l, which, as the elevation is 800 feet, is
probably very near the truth.
Mr. Garside has sent an observation of temperature taken by himself
in the roof of the Mersey tunnel in August 1883. The temperature was
53°, the depth below Ordnance datnm being 92 feet. A great quantity
of water from the river was percolating through the sides of the tunnel.
On Auoust 13, 1884, he verified his previous observation in Denton
Collieiy (Ibth Report). The second observation was made at the same
depth as the first (1,317 feet), in the same pit and level, and under the
same circumstances, except that the thermometer was allowed to remain
fourteen days in the hole bored for it, instead of only six hours. The
temperature observed was the same as before, namely 66°.
Mr. Garside has also supplemented his previous contribution to our
knowledge of the surface temperature of the ground in the East Man
chester coalfield (16th Report) by two more years' results from the
same observing stations. The following are the collected results, includ
ing the year previously given : —
Croft House, in the centre of AsJdmiunderLjjne, 345 ft. above sea.
I
— 4 ft. Deep
1 ft. Deep
Mean of Max.
and Min. Air
1882
1883
1884
47°5
46° G
4S°3
46°2
45°o
47°3
48°4
47°8
48°9
Means
47°5
46°3
48°4
District Ivfirmary, 501 ft. above sea.
—
4 ft. Deep
1 ft. Deep
Mean of Max.
and Min. Air
1882
1883
1884
45°9
46°3
470.7
4.5°6
45°3
47° 3
46°6
46°3
48°2
Means
4€°6
46°1
47°0
Giving equal weight to the 4foot and 1foot observations, we have a
mean surface temperature of 46°9 at an elevation of 345 feet, and 46°4
ON THE EATK OF INCIIEASE OF 0x\DERGKODND TEMPEllATUUK. i>7
at 501 feet. The diBFerence between them agrees well with the generally
accepted rate of 1° for 300 feet, and indicates about 48° as the surface
terapsrature at small elevations, such as 30 feet. The pits in the East
Manchester coalfield from which we have observations, namely, Astley
Pit (Uakinfield), Ashton Moss, Bredbury, Denton, and Nook Pit, are all
sunk in ground at elevations of between 300 and 350 feet. It would
therefore appear that the assumption of a surface temperature of 49°,
which wc made in reducing these observations, is about 2° in excess of
the truth.
A very elaborate paper on Underground Temperature has recently
been communicated to the Royal Society by one of the members of the
Committee — Professor Prestwich. It contains probably the fullest col
lection that has ever been made of observations of underground tempera
ture, accompanied iu most cases by critical remarks ; and adduces
arguments to show that most of the temperatures observed are too low,
■owing to the influence of the air in mines, and of convection currents in
wells. Professor Prestwich is disposed to adopt 1° F. in 43 feet as the
most probable value of the normal gradient.
Report on Electrical Theories.
By Professor J. J. Thomson, M.A., F.R.S.
In this report I have confined myself exclusively to the consideiation of
those theories of electrical action which only profess to give mathematical
■expressions for the forces exerted by a system of currents, and which
make no attempt to give any physical explanation of these forces ; for it
is evident that before we can test any theory of electrical action we mu.st
know what the actions are \vhich it has to explain, and we cannot do this
until we have a satisfactory mathematical theory. 1 have further limited
myself to the consideration of the fundamental assumptions of each
theory, and have not attempted to give any account of its mathematical
developments, except in so far as they lead to results capable of distin
guishing between the various theories.
I have divided the theories into the following classes : —
1. Theories in which the action between elements of current is deduced
by geometrical considerations combined with assumptions which are
not explicitly, at any rate, founded on the principle of the Couservatioii
of Energy.
This class includes the theoi'ies of Ampere, Grassmann, Stefan, and
Kortewee.
2. Theories which explain the action of currents by assuming that
the forces between electrified bodies depend upon the velocities and accele
rations of the bodies.
This class includes the theories of Gauss, Weber, Riemann, and
Clausius.
3. Theories which are based upon dynamical considerations, but which
neglect the action of the dielectric.
This class contains F. E. Neumann's potential theory and v.
Helmholtz's extension of it.
4. C. Neumann's theory.
1.88.5. H
98 REPOET — 1885.
5. Theories which are based upon dynamical considerations, and which;
take into account the action of the dielectric.
This class includes the theories of Maxwell and v. Helmholtz.
We shall now proceed to the detailed consideration of these theories.
Theories in which the action between elements of current is deduced hy
geometrical considerations combined with certain assumptions which
are not e.rplicitly, at any rate, foutuled on the Principle of the Conser
vation of Energy.
The best known theory of this class is that of Ampere. Others,
however, have been given by Grassmann, Stefan, and Korteweg, which
we shall consider in order.
Am,pere's Theory.
This theory was first published in 1820. In 1823 appeared his great
paper, the ' Memoire sur la Theorie Mathematique des Phenomenes
Electrodynaraiques,' Memoires de VInstitut, t. vi., which Maxwell de
scribes as ' perfect in form and unassailable in accuracy,' and which at
once brought the action between electric currents under the power of
mathematics. Ampere founded his theory on certain postulates which
he attempted to establish by experiment ; inasmuch, however, as he
always dealt with closed circuits in his experiments and elements of
circuit in his postulates, the experimental evidence is not quite satis
factory. Ampere's experiments have been repeated by v. Ettingshausen ^
with much more delicate apparatus.
The postulates used by Ampere are as follows. The first four are
given in the words of Professor Tait : — ^
I. ' Equal and opjoosite currents in the same conductor produce equal
and opposite effects on other conductors ; whence it follows that an
element of one current has no effect on an element of another which lies
in the plane bisecting the former at right angles.'
II. ' The effect of a conductor bent or twisted in any manner is
equivalent to that of a straight one, provided that the two are traversed
by equal currents and the former nearly coincides with the latter.'
III. ' No closed circuit can set in motion an element of a circular
conductor about an axis through the centie of the circle and perpendicular
to its plane.'
lY. ' In similar systems traversed by equal currents the forces are
equal.'
Y. ' The action between two elements of current is a force along the
straight line joining them, and proportional to the product of the lengths
of the elements and the currents flowino' through them.'
It follows from IV. that the force between two elements of current
varies inversely as the square of the distance between them.
The assumption Y. is one that can only be justified by the correctness
of the results to which it leads. We have no right to assume i^t priori
that the action is equivalent to a single force, and not to a force and a
couple : and we have no more right to assume that the force is along the
line joining the elements than we have to assume that the force between
' ' Ueber Ampere's elektrodynamische Funclamentalversuche,' Wicn. Ber, (11), 77,.
p. 109, 1878.
 Tait's Quaternion?, 2nd edit. p. 249.
ON ELECTRICAL THEORIES. 99
two small magnets is along the line joining their centres, and in this case
the assumption is untrue. It is in the nature of the assumption V. that
Ampere's theory differs from others of this class. The second part of
T. depends upon V. It is not true unless we assume that the force
between two elements is along the line joining them.
Ampere deduces the force between two elements of current from these
principles in the following way : — Suppose we have two elements of current
of lengths dsi, ds^ traversed by cuirents of strengths i, j respectively.
Let us take the line joining the centres of these currents as the axis of x ;
let the plane of c?s, and x be taken as the plane of xy ; let 0,, 6^ be the
angles which cZs,, ds^ respectively make with the axis of x, rj the angle
which the plane through tZs., and ;• makes with the plane of xy.
By Ampere's second pi'oposition the action of ds^ on ds.2 will be the
sum of the action of
f fZ^i cos d^ or a, along x
\ d'*i sin ^1 or /3i along y
on
ds^ cos 02 01* "2 along x
ds2 sin 02 t'os V or ft^ along y
ds2 sin 02 sin ?/ or yg along z.
Now by proposition I. «[ cannot exert a force on either /Sg or 72*
because it is in planes which bisect /j, and y.y at right angles, so that the
only component on which a^ can exert a force is u^. Let the force between
these components be
a
2«l«2
■where r is the distance between the centres of the elementary currents.
In the same way we can show that the only component on which /3,
can exert any force is jo.2 I^^t the force between these two elements be
^ ,•> a
r
Thus the force between the two elements ds^, ds^ is
— (aai«2 + 6/3 1/3 2},
or, substituting for a^a^, r'lftz their values :
J [a cos 0, cos 92 + h sin 0i sin 09 cos tj} ij f?Si cZsg.
The proposition III., that the action of a closed circuit on an element of
current is always at right angles to the element, leads on integration to
the condition
2a + i = 0,
so that the force between the two elements equals
jj {cos 01 cos 02 — 2 sin 6^ sin 00 cos t]] ijdsy ds^.
IFrom this we ai'e able to find the force between any two circuits or parts
of circuits To find the force on a magnetic system, Ampere used his
H 2
100 EEPORT— 1885.
principle that the magnetic action of an electric current was the same as
that due to a magnetic shell bounded by the circuit and magnetised to
the proper intensity. In this way Ampere gave a complete theory of the
action of currents upon currents and upon magnets — in fact, a complete
theory of all the effects produced by a current which were known when
his paper was published.
It is difficult to overrate the service which Ampere's theory has
rendered to the science of electrodynamics. Perhaps the best evidence
of its value for practical purposes is the extreme difficulty of finding any
experiment which proves that it is insufficient. In spite of this, how
ever, as a dynamical theory it is very unsatisfactory. If, as we are led
to do by Ampere, we attach physical importance to elements of current,
and regard them as something more than mathematical helps for calcu
lating the force between two closed circuits, then we are driven to ask,
not only what is the law of force between the elements, but what is the
energy possessed by a system consisting of two such elements. If we do
this, and find this energy by calculating the amount of work required to
pull the elements an infinite distance apart, we arrive at the conclusion
that the energy must depend upon the angles which the elements make
with each other and with the line joining them ; but if this is so, then
the force between the elements cannot be along the line joining them,
and there must in addition to this force be couples acting on the elements.
For these reasons we see that Ampere's theory cannot give the complete
action between two elements of current. What it does — and this for
practical purposes is an advantage and not a disadvantage — is to give
in most cases, instead of the complete action between two elements, that
part of it which really affects the case under consideration.
Before discussing cases, however, in which the terms which Ampeie
neglects might be expected to produce measurable effects, we shall, in
order to compare the various theories more easily, proceed to consider
other theories of the same class.
Grassmann's Theory.^
The method by which Grassraann obtains his theory is very remark
able. He objects to Ampere's formula for the force between two elements
of current, because it makes the force between two parallel elements
change from an attraction to a repulsion when the angle which the ele
ments make with theline joining them passes through the value cos~' 2/3,
and the object of his investigation is to get a law of foi^ce free from this
peculiarity, and which, while giving the same result as Ampere's for closed
circuits, shall yet be as simple as possible. He begins by regarding any
circuit as bailt up of ' Winkelstrome,' i.e., currents flowing along the two
infinite lines which form any angle. He points out that a circuit of any
shape can be built up of such currents ; the circuit ahc, for example,
may be regarded as built up of the ' Winkelstrome ' eaf, fbg, and gee.
Grassmann proceeds to calculate by Ampere's formula the action of
a ' Winkelstrom ' upon an element of current («). Since the 'Winkel
strom ' will have no action upon an element of current perpendicular to
its plane, we see that it is only necessary to calculate its action upon the
component (a') of a in its own plane. Grassmann does this by calcu
lating the effect due to each arm of the ' Winkelstrom ' separately. He
' Fogg. Ann. Ol, p 1, 1815 ; Crelle, 83, p. 57
ON ELECTIUCAL THEORIES.
101
finds expression for the forces along and perpendicular to a', due to an
infinite rectilinear current starting from a definite point. The force of
such a current along a' does not depend on the angle the current makes
with the line from its end to o', so that the effects of two such currents
starting from the same point and flowing in opposite directions, i.e. of a
' Winkelstrom,' will be to produce no force along o' ; thus the effect of a
' Winkelstrom ' on an element of current in its own plane will be a force
at right angles to the element. The force at right angles to a' due to a
rectilinear current will consist of two parts, one independent of the angle
made by the current with the line joining its end to the element, the
other depending upon this angle. The first part will vanish when we
consider a ' Winkelstrom ' ; the second part only will produce any effect.
Now Grassmann says that it will much simplify the analysis, and obviously
(since any closed circuit may be built up of 'Winkelstrome ') lead, for
closed circuits, to the same result as Ampere's formula, if we suppose that
the law of force between elements of currents is such that the only effects
produced by a rectilinear current are those which do not vanish for a
' Winkelstrom,' and hence that a straight current exerts on an element of
current a force at right angles to the projection of the element on the
plane containing the centre of the element and the rectilinear current,
and that the magnitude of this force is
ij ds'
cot
2'
where i is the sti*ength of the rectilinear cnnent, y the strength of the
102 KEPORT — 1885.
element of current, ds' its projection on the plane through its centre
containing the straight current, r the distance of the element from the
end of the straight current, and o the angle which the rectihnear
current makes with the line joining its extremity to the elementary
current. By taking the difference of two such rectilinear currents,
Grassmann finds the action of an element (/3) of current on another
element («) is a force at right angles to a', the component of a in the
plane containing /3 and the middle point of a and equal to
. . dads' ■ n
^3 72 «^^ ^'
where is the angle which /3 makes with r, da the length of (/3), and j the
current flowing through it.
The direction of the force is along AB, where A is the centre of the
element (a) and B the point where the normal to a' is cut by /3 produced
in the direction of the current.
If we treat this theory in the same way as we did Ampere's on p.
99 by considering the action of the component a,, /3i of an element of
current ds, on the components 02, /^o, 72 of another element ds.,, we see
that Grassmann's theory is equivalent to supposing that a, exerts no
force on a^, ft.^, or 72 ; i^l^at ft^ exerts a force A/JjUo on u^ at right
angles to a.^ in the plane of xxj, and a force A/3i/32 on /32 at right angles
to it, that is, along the line joining the element, and that it exerts no
force on y^ ....
Thus we see that Grassmann's theory :s equivalent to replacmg
Ampere's assumption, that the force between two elements of current
acts along the Hue joining them, by the assumption that two elements of
current in the same straight line exert no force on each other.
As a dynamical theory of electrodynamics, Grassmann's theory is open
to the same objection as Ampere's, that it does not take into account the
couples which may exist between the elements, and also to the additional
objection that, according to it, the action of an element of current ds^ on
another element ds.^ is not equal and opposite to the action of ds^ on
dsi, so that the momentum of the two elements cZs, and ds.^ will not
remain constant, and, as the theory does not take into account the sur
rounding ether, there is no way of explaining what has become of the
momentum lost or gained by the elements. As a piece of geometrical
analysis, however, the theory is very elegant and worthy of the author of
the ' Ausdehnungslehre.'
From the way in which Grassmann's theory was developed we see
that between closed circuits it must give the same forces as Ampere's ; for
unclosed circuits this is not the case, and Grassmann, at the end of the
paper quoted above, mentions a case where the two theories would give
opposite results, assuming that unclosed streams exist. Suppose we have
a magnet //s and an unclosed current AB in the same plane as the
magnet and passing through its middle point, then if Ampere's theory
be true, the magnet will twist in one direction ; if Grassmann's, it will twist
in the opposite. This depends upon the change, according to Ampere's
theory, of the force between two parallel elements from attraction to repul
sion, when they make the angle with the line joining them at less than
sin' 1 / v/'3', while according to Grassmann's theory, there is no such
change.
ON ELECTRICAL THEORIES. 103
Stefan's Theory}
This resembles Ampere's theory very closely, except that Stefan does
•not make the assumption that the force between two elements of current
is along the line joining them : this difference leads to the introduction
of two forces which Ampere neglects.
We shall use the same notation as when we discussed Ampere's
theory, and consider, as before, the action of an element of current dsi
on another element dso. Stefan, like Ampere, assumes that we may
replace an element of current by its component, so that we have to con
sider the action of the components («,, /^i) of ds^ on the components
(«2) ^21 yi) of c7S.
As in Ampere's theory, the component a, is supposed to exert a force
r2
on a 2, this force by symmetry must be along the line joining the
elements.
a, is supposed to exert a force on ji^ equal to
along the axis of y. We can see that this force may exist, for it is
conceivable that it should be in the same direction as jl.2 when a, points
from the middle of ds^ to the middle of ds<i, and in the opposite direction
to 1^2 when ctj points in the opposite direction. Stefan assumes that a^
exerts no force on /32 parallel to the axis of z, and no force at all on 72
/jj is supposed to exert a force on uo parallel to the axis of y and
equal to
d ,
r
We may see, by the same reasoning as we used before for the force
between /J, and «2> that it is conceivable that this force may exist. /3i is
supposed to exert no force on 05 parallel to the axis of z.
As in Ampere's theory, /ji is supposed to exert a force on j32 equal to
^ . ,
^Pilh,
this force must by symmetry be along the line joining the elements ; /3,
is supposed to exert no force on 72
Thus the action of ds^ on dsg consists of a force
72 ani«2+ ^Pi/32 j
.along the line joining the elements, and a force
72 c«i,'32 + cZ/3i"2
at right angles to this line in the plane containing dsi and r. If we take
' Stefan, Wien. Sitzungshcriclde, 59, p. 693, 1SG9.
104
REPOllT 1885.
arbitrary coordinate axes and suppose that .v, y, z are the coordinates of cZs,^
a;', 2/', z' those of ds.,, then the x component of the force on ds2 due to dn^
is shown by Stefan to be equal to
d
'■^''^''^^'M^^^rjr
(a;' — x) d 1 dx^ d
r dni r ds.2 ^
__ 1 dx
dso r da.
3=1^
+ 2
cost
■with similar expressions for the force parallel to the axes of y and z.
Here /, j are the currents through
between the elements of current, and
')n:=
3 l"
•C
ds2 respectively, £ is the angle
n=l{ahc + 2d}
f= —^{ii — h + 2cd]
q=^[a + 2hcd].
We see from this expression for the force parallel to x that the last
term is the only one which does not vanish when integrated round two
closed circuits of which ds, and ds^ are elements. So that the force will
depend only upon // ; the value of q will depend upon the units we adopt :
in Stefan's work q is put equal to —1/2.
This is the only condition to be got by considering the translatory
foi'ce between two circuits ; we can get another by considering the couple
acting on the closed circuit, supposed rigid, of which ds^ forms a part.
For the s component N of this couple Stefan finds the expression
c7ii'' dy _dy^ dx
N
= U2fP
y^x — x^y
cos £ dsids2 — 1
JP
'fir c7ii'' dy _dy^ ^•'' 1 i
J r \ ds^ ds^ ds2 ds^ J
c?>,.
But supposing the two circuits to have a potential
U
cos £
p:
ds■^ ds.,,
we can easily see that the couple
. . rr.'/'.v.'y'y
= IJ ;3  cos £ dSidS.2
n
'llL _ ^'^\ 7 ,
c/s, ds, dsa ds, ' ' 1 ■ '^
'2
1
i
thus if two circuits have a potentij
or substituting fovp and q their values,
2a + b + C2d^0.
If c=0 and (.7=0, as in Ampere's theory, this relation becomes
2a + b = 0,
which is the same relation as Ampere deduced by finding the condition
that the foi'ce due to a closed circuit on an element of current should be
at right angles to the element, and Stefan has proved that on his theory
the same condition leads to the equation
p = q,
i.e., the same condition as the one which expresses that two closed circuits
have a potential.
ON ELECTRICAL THEOUIES. 105
Stefan shows that, fi'om the consideration of the action of closetT.
circuits on elements of other circuits or of themselves, it is impossible to
get any other relation between the quantities a, b, c, d, so that we have
only two relations between the quantities a, h, c, d, and thus two of them
must be indeterminate.
We may give any values we please to these quantities, provided the}
satisfy these two relations ; if we put c = 0, c? = we get Ampere's theory ;
if or, ^ 0, c = 0, Grassmann's ; and we can get a number of other theories by
giving different values to these quantities.
Stefan's theory is open to the same objection as Ampere's, since it
does not take into account the couples which one element may produce
on another. He also limits the generality of his theory by supposing that
the force between two elements of currents in one plane is in that plane.
Korteicey's Theory.^
According to this theory, the forces between two elements of current
are the same as in Stefan's theory ; Korteweg, however, considers in
addition the couples which one element may produce on another.
If we use the notation we adopted in discussing Stefan's theory, we
have, considering the force on dso, a force
along the line joining the elements, and a force
parallel to the axis of y.
In addition. to these forces, Korteweg supposes that from the action of
«! on /Bj there is a couple whose axis is parallel to the axis of z equal to
and from the action of «i on y^ a couple on yg whose axis is parallel to
the axis of y and equal to
/ar/2;
from the action of /Jj on a 2 there is a couple on a. 2 whose axis is parallel
to the axis of '4 and equal to
and from the action of /^i on y^ there is a couple on y., whose axis is
parallel to the line joining the elements and equal to
A/3,02.
If we now take arbitrary coordinate axes, the forces on the element d,,
are the same as those given by Stefan's theory. The couples, however, are
different. The component parallel to the axis of x of the couple 011
ds2 is given by the equal iuti
_r2 d,2 \ ./., cL^J r* ds2 ds ^'' "^^
' Crelle, xc. p. 49, 1881.
lOH EEPORT — 1885.
(h + a) dr / , , s dz, , , . dij'^ \
r dsi L (li<2 "*2 J
7 / f'//' ''■s dy dz "1 ~
I (Is 2 dsi dni ds2 J J
ii dsi ds2,
with similar expressions for the components of couple around the axes of
y and z.
By making the force between two closed circuits have the same value
as that given by Ampere's theory, Korteweg finds that
a + 2bdc =  3A2,
where A is a constant quantity whose value depends upon the unit of
current adopted.
By making the couples produced by one closed circuit on another
have the same value as that given by Ampere and the potential theory,
he finds that
i ('•''^0 + (iZ^O rc + 2A2 = 0.
dr
Korteweg considers that the experiments of v. Ettingshausen, quoted
above, prove (1) that the force on an element of circuit produced by a
closed circuit is at right angles to the element, and (2) that the couple on
an element due to a closed circuit has the value given by Ampei'e's theory.
The first condition gives
ch = 2A2;
the second the two conditions
h + g = 0.
And he points out that we cannot get any more conditions by consi
dering the action between two closed circuits, or the action of a closed
circuit on an element of another.
It should be noticed that since, according to this theory, part of the
action of one element of a circuit on another consists of a couple, the
condition that the force due to a closed circuit on an element of another
should be at right angles to the element is not, as in Stefan's theorj', iden
tical with the condition that the expression for the couple exerted by one
closed circuit on another should be the same as that given by Ampere.
This theory is valuable because it is the most general one of the class
we are considering which has been published. It is the only one which
takes into account the couples, and by giving special values to the quan
tities a, h, c, d,f, g, h, we can get any of the other theories of this class.
ON ELECTRICAL TIIEOinES. 107
■On the theories which explain the action of currents hij assuming that the
forces beticeen two electrified bodies depend upon the velocities and ac
celerations of the bodies.
According to these theories a body conveying an electric current con
tains equal quantities of positive and negative electricity, so that it will
Dot exei't any ordinary electrostatic eifect : the positive electricity is sup
posed, however, to be moving differently from the negative. In some of
the theories (Weber's, Gauss's, Riemann's) Fechner's hypothesis, that the
electric current consists of positive electricity moving in one direction
(the direction of the current), and an equal quantity of negative elec
tricity moving at the same speed in the opposite direction, is assumed ;
in other theories (Clausius') only one of the electricities is supposed to
move, the other remains at rest. We can see in a general way how the
assumption that the forces between two electrified particles depend on
the velocities and the accelerations of the particles can explain the effects
produced by an electric current.
Let us take first the mechanical action between two circuits A and B,
and let us consider the action of an element (a) of A on an element (6)
of B. We shall consider first the action of the two electricities which are
flowing through a on the positive electricity which is flowing through b.
Since the motion of the positive electricity in a relative to that of the
positive electricity in b is not the same as the motion of the negative
electricity in a relative to that of the positive in b, the forces due to the
positive and negative electricities in a will not counterbalance, so that
there will be a resultant force on the positive electricity in b depending
on the inequality between the motion of the positive and negative
electricities in a relative to that of the jjositive in b. Similarly there
will be a force on the negative electricity in b depending on the in
equality between the velocities of the positive and negative electricities
in a relative to that of the negative in b, and, except for special laws of
force and special values of the velocities of the electricities in b, this force
will not be equal and opposite to the force on the positive electiicity in b,
so that a mechanical force on b will be produced by the currents through a.
Let us now consider how inductive forces can be explained by this
hypothesis : let us suppose that the element a is moving, and that the
element b is at rest. The velocity of the electricity in a will be the
resultant of the velocity with which the electricity flows through a and
the velocity of translation of a itself, so that since the velocities of flow
•of the positive and negative electricities are different, the actual velocity
of the positive electricity will differ in magnitude from the velocity of
the negative (unless, assuming Fechner's hypothesis, the element a is
moving at right angles to itself) ; thus the force due to the positive
electricity in a on a unit of positive electricity at b will not be equal and
opposite to that due to the negative electricity in a, and thus there will
be an E.M.F. at b due to the motion of a. This explains induction due to
the motion of the primary circuit.
Let us now consider induction due to the variation of the intensity of
the current in the primary circuit. According to all the theories there
IS a force produced by a moving electrified body proportional to the first
power of the acceleration of that body. Let us consider the elements a
and b again, and suppose that a variable current is flowing through a and
BO current through b ; then if we suppose that a variation in the intensity
108 KEi'oia — 1885.
of a current is accompanied bj an alteration in the velocity of flow^
the acceleration of the positive electricity will, if we take Fechner's
hypothesis, be equal and opposite to that of the negative ; but since there
is a part of the force due to the moving electrified body which changes
sign both with the electrification and the acceleration, the force due to
the acceleration of the positive electricity will be equal in all respects
to that due to the acceleration of the negative, so that there will be a
resultant force on a unit of positive electtiuity at h, and this foi'ce is the
electromotive intensity at b due to the alteration of the intensitj^ of the
current in a. In this way we can explain the induction due to the varia
tion of the current in the primary circuit.
Theories of this kind have been given by Gauss, Weber, Riemanu,
and Clausius, and these writers have given expressions for the force
between two electrified particles moving in any way. We shall after
wards consider these expressions in detail, but we may remark in passing
that the theories of Gauss, Weber, and Riemann have much in common ;
among other things they all lead to impossible results. In addition
Clausius has shown that, unless we make Fechner's hypothesis about a
current, viz. that it consists of equal quantities of positive and negative
electricity moving with equal speeds in opposite directions, a current would
on these theories exert a force on an electrified body at rest.
The question of the forces due to moving electrified bodies is
interesting in connection with electrolysis. Taking the ordinary view
that the current is carried by the ions, we know from Hittorf 's researches
that the anion and the cation move at different rates, so that the forces
produced by these will be different ; hence we should expect an electrolyte
conveying a current to exert a force on a charged particle at rest.
We shall now go on to consider the various theories separately.
Gauss's Theory.^
Gauss assumes that the force between two particles separated by a
distance r and charged with quantities of electricity e and e' is along the
line joining the particles and equal to
where ii is the relative velocity of the two particles and c is a constant.
This law will, if we make Fechner's hypothesis, explain the mecbanical
force between two circuits ; but, since it contains no term depending on
the acceleration, it cannot explain the E.M.F. produced by the variation
of the strength of the current in the primary ; it is also inconsistent with
the principle of the Conservation of Energy, and so we need not consider
it any further.
W. E. Weler's Theory.^
Weber assumes that the force between two charged particles, usiug
the same notation as before, is
ee
r
^{^M'SK;:fr)}
' Gauss's theory was published after his death in his collected works, Gottingen
edition, vol. v. p. 616. See also Maxwell's Electriclfi/ uivl Maijncthiit, 2ud edit, vol,
ii. p. 440.
 Weber's theory was published in 1846 in Abhundluwjeii der KdmglichSdch^
ON ELECTRICAL THEORIES, 109
This fonnnla is not inconsistent witli the principle of tlie Consei'vation of
Energy ; making Fechner's hypothesis, it will explain the mechanical force
between circnits conveying currents ; it will also exjilain induction due
both to the motion of the primary and the alteration in the strength of the
current in the primary. We shall see, however, that it makes a body
under certain circumstances behave as if its mass were negative ; i.e. if it
were acted on by a force in a direction opposite to that in which it is
moving, its velocity would continually increase.
Riemann'.s Theory.
This is explained in his ' Schwere Electricitat uud Magnetismus,'
edited by Hallendorff, p. 327. According to this theory the force be
tween two electrified bodies is not altogether along the line joining them,
but consists of the following parts : —
1. A force along the line joining the particles equal with the same
notation as before to
?'{i'l}
2. A force on the first particle parallel to its velocity relative to the
second equal to
2ee' dr
oh^'^di
3. A force on the first particle parallel to its acceleration relative to
the second equal to
f,
c'r
where /is the relative acceleration of the particles.
There are of course similar forces acting on the second particles, and
we see from the form of the expressions of the forces that the force on the
first particle is equal and opposite to the force on the second. Riemann's
law of force is not inconsistent with the principle of the conservation of
energy, and it explains the mechanical force between two circuits ; hence
it must explain the induction of currents. We shall see, however, that it
is open to the same objection as Weber's theory, viz. that it makes an
electrified particle under certain circumstances behave as if its mass were
negative.
Glausius' Theory.^
If X, y, z are the coordinates of the first electrified particle, x' , y', z'
those of the second, then according to this theory the x component of the
force on the first particle is equal to
— ee'x — < (J —vv cos i c^)~ > — r (  — 1
[dxX^ ' \l c^ dt\r dtj]
With similar expressions for the components parallel to y and z, here
jslschen Gesellscluift der WissenscMften, 18ifi, p. 211 ; it is reprinted in Electro
dynamische Maassbestimmnnijen, 1871. A good account of the theory is given in
Maxwell's Electricity and Maynetimn, 2nd edit. vol. ii. chap, xxiii.
' This theory is given in Crelle, vol. 82, p. 85. There is also a fuU abstract in
"Wiedemann's Beibldtter, vol. i. p. 143.
to
110 BEPOET — 1885.
V and v' are the velocities of the first and second particles respectively,
and E is the angle between their directions of motion. We may analyse
these forces a little differently, and say that the force on the first particle
consists of —
1. A force along the line joining the pai'ticles equal to
ee' f , , ; 1
2 s J —vv cosejv >
2. A force parallel to the velocity of the second particle and equal
ec' <h ,
3. A force parallel to the acceleration of the second particle equal
to
ee' dv'
~'d^ 'df'
We have, of course, corresponding expressions for the force on the second
particle.
Clausius' formulae differ from those of Gauss, Weber, and Riemann
in two very important respects.
1. They mike the forces between two electrified bodies depend on the
absolute velocities and accelerations of the bodies, while the others make
them depend only on the relative velocities and accelerations.
2. They do not make the forces between the bodies equal and oppo
site, so that the momentum of the system does not remain constant.
These results show that if this theory is ti'ue, we must take the ether
surrounding the bodies into account. The first result can then be
explained by supposing that the velocities which enter into the formulis
are the velocities of the bodies relatively to the ether at a considerable
distance from the bodies, and the second result by supposing that the
ether possesses a finite density, and that the momentum lost or gained by
the bodies is added to or taken from the surrounding ether.
The case is analogous to the case of two spheres A and B moving in
an incompressible fluid ; in this case the forces on the sphere A depend
on the velocities and accelerations of B relatively to the fluid at a great
distance from the sphere, and aie independent of the velocity and accele
ration of A ; the forces are not equal and opposite, and the momentum
lost or gained by the system is added to or taken from the momentum of
the fluid. At the end of this section we shall see that, if we assume that
variations in what Maxwell calls the electric displacement produce effects
analogous to those produced by oidinary conduction currents, we get
the same forces between moving electrified bodies as are given by Clausius'
theory.
Clausius' theory is not inconsistent with the principle of the con
servation of energy, and we shall see that it does not lead to the same
diSiculty as the theoi'ies of Weber and Riemann, viz., that under special
circumstances a body would behave as if its mass were negative.
Assumino that in an electric current we have equal quantities of
positive and negative electricity moving with different velocities, Clausius
has shown in the paper already cited that his theory gives Ampere's
results for the mechanical force between two circuits, and the usual
ON ELECTKICAL THEORIES. Ill
expression for the induction due to tlie motion of the primary circuit, or
variation in the strength of the current passing through it.
Frohlich ' urges against Clausius' law that since, according to it, an
electric current in motion exerts an electromotive force on a moving
electrified particle, even though the particle is moving at the same rate
as the circuit, every current on the earth's surface ought to exert an
electromotive force on an electrified particle relatively at rest, since each
is moving with the velocity of the earth. This force is one that can
be derived from a potential, so that the integral of the force taken round
a closed curve would vanish, and thus, even if this result were true, two
circuits would not induce currents in each other if they were relatively
at rest. Budde points out, however, that the moving circuit would exert
an electromotive force at each point of itself, and thus cause a separation
of the electricity in the circuit, so that it would get coated with a distri
bution of electricity, the electrostatic action of which would balance that
due to the action due to its motion on a point relatively at i^est. The
velocities which enter into Clausius' formulje are velocities relative to the
ether, so that if the ether moves with the earth, an electric current will,
according even to this theory, exert no electromotive force on a point
relatively at rest, and there will be no electrification on the surface of
the circuit. The velocity c which occurs in all these theories is a velocity
comparable with the velocity of light.
General Considerations on these Theories.^
We shall now go on to discuss a general way of treating theories of
the kind we have been considering. Perhaps the best way of doing this
is to consider not the forces between the electrified bodies, but the energy
possessed by them. If the energy depends on the electrification there
will be forces between two electrified bodies. Now the potential energy
depends on the electrification, and this dependence produces the ordinary
electrostatic forces between two electrified bodies at rest. If, however,
the kinetic energy as well as the potential depends on tlie electrification,
then the forces between two electrified bodies in motion will be different
from the forces between the same bodies at rest. An easy way of seeing
this is by means of Lagrange's equations.
If T be the kinetic energy, and x a coordinate of any kind, then we
have, by Lagrange's equations,
— — — = external force of type x.
dt dx dx
Hence if we have any term T' in the expression for the kinetic energy,,
■we may, if we like, regard it as producing a force equal to
_ ^J^' + ^
dt dx dx
A simple illustration of this is afforded by the centrifugal force. In
» Frohlich, Wied. Ann., ix. p. 277, 1880.
* Wied. Ann., s. p. 553, 1880.
' See Clausius ' On the Employment of the Electrodjnamic Potential for the
Deterrnination of the Ponderomotive and Electromotive Forces,' I'kil. Mag., 1880, v.
10, p. 255.
112 REPORT— 1885.
the expression for the kinetic energy of a moving particle there is the
term
■where r is tHe distance of the pai'ticle ivo'.n some fixed point, and d the
angle which the i^adius from this point to the particle makes with some
fixed line ; m is the mass of the particle. This terra, by the above rale,
will give rise to a force of type r, i.e., along the radius vector equal to
and this is the ordinary centrifugal force.
Now let us consider a moving electrified body. If it is symmetrical,
■and moves in an isotropic dielectric, it is evident that the electrification,
if it enters at all, can only enter as a factor of the total velocity y,
and cannot affect the separate components of the velocity differently.
Let us suppose that the body is charged with a quantity of electricity
denoted by e, then the kinetic energy, if it depends on the electrification,
.must be of the form
•where /(e) denotes some function of e. Now /(e) must be always
positive, for if it were negative we could make
\m + f{e)
negative, and then the electrified body would behave like one of negative
mass. The simplest form satisfying this condition which we can take for
/■(e) IS ae^, where fi is some positive constant ; so that the form of ex
pression for the kinetic energy may be taken as
Now let us go on to the case where we have two electrified bodies present,
with charges e and e' of electricity ; let m and m' be their masses, q, q'
their velocities, of which the components parallel to the axes of x, y, z
nre (n, v, w)' ("'' ''^' ■> '^') respectively, the coordinates of the particles
being (.r, ?/, z), (a;'_, 7/, s') .
If everything is symmetrical, the expression for the kinetic energy,
if it only involves second powers of the charges of electricity, will be of
the form
\m(^ + \mcp + cie^^ + /5e'^ ^'^fee' k ./ {u, v, iv, «', v', w'}
where/ (it, v, xv, n', v', iv') is a quadratic function 0? u, v, lu, u', v', w'.
By Lagrange's equations we see that the last term will give rise to a
force parallel to the axis of .r on the particle whose charge is e equal to
I. dx dt du J
with similar expressions for the forces parallel to ij and z. We can
see, by substituting in this expression, that we get Weber's law if we
make
/ =  < (lo — u') + 2 ^ [v — v') + (to ~ w') \ ;
r I r r r J
ON ELKCTRICAL THEORIES. 113
Riemann's law, if we make
/= I {(u  ti'y + (v v'y + (w  w'y] ;
Clansins' law, if we make
f=~ {mm' + vv' + ww'\ ;
and that we cannot get Gauss's law in this way ; this is in accordance
with the fact that Gauss's law does not satisfy the principle of the
conservation of energy. This way of considering the theories enables us
to see that neither Weber's nor Riemann's formulae can be right, for if
they were, an electrified body, when in presence of another, would, under
certain circumstances, behave as if its mass were negative. Thus take
Weber's law as an example : let us suppose that two electrified bodies are
moving along the line joining them, which we may take as the axis of x ;
then the expression for the kinetic energy, putting in the value of / which
corresponds to Weber's law, is
so that if im + ae2 + ^
r
be negative, then the coefficient of if in the kinetic energy will be nega
tive, and the body will behave as if its mass were negative ; and, by
sufficiently increasing e' or diminishing r, we can make this expression
negative, so that Weber's law leads to results which are inconsistent with
experience. This result of Weber's law was first pointed out by Helmholtz. '
Exactly the same objection applies to Riemann's theory, and indeed
we see that it will apply to any theory which makes the force between
two electrified bodies depend on relative velocities and accelerations.
The same objection need not apply to Claasius' theory, for substitut
ing the value of/ belonging to his theory, the kinetic energy equals
{\m + ae2)22+ (i„i' + /3e'2)2'2 + ^^^, qq' cos e
r
so that the kinetic energy will be always positive if
ilm + ae') (hn' + l3e'^)>ff£l^.
This condition will evidently be satisfied if
and this relation does not involve the electrification. We cannot assume
that we can make r so small that this condition is not satisfied, for r has
a minimum value depiending upon the shape and size of the electrified
bodies. For example, if these are spheres, r cannot be less than the
sum of their radii. On the other hand, a and /3 may be functions of the
' Ueber die Tlworie der EleUrodynamik. Crelle, vol. Ixxv. p. 635 • Collected
Works. Bd. I, S. 647.
1885.
114 BEPOET — 1885.
sizes of tte electrified bodies, and the geometrical relations may be such.
that the condition written above must be always satisfied.
Fliysical reasons why the force between two electrified bodies should depend
on their velocities and accelerations.
If we assume Maxwell's hypothesis that a change in the electric
polarisation produces the same effect as an electric current, then we see
that the kinetic energy of an electrified body must be different from the
kinetic energy of the same body moving at the same rate but not electri
fied. For let us suppose that we have an electrified body at rest, and
consider the amount of work necessary to start it with a velocity q^. It
is evident that it will be greater than when it is not electrified, for when
it is electrified and in motion the electric polarisation in the surrounding
dielectric will be in changing, and so in addition to starting the body
with a velocity q we have, if Maxwell's hypothesis be true, to establish
what is equivalent to a field full of electric currents. The production of
these currents of course requires work, so that more work is required to
start the body with a velocity q when it is electrified than when it is not ;
in other words, the kinetic energy of a moving electrified body is greater
than that of one not electrified, but under similar conditions as to mass and
velocity. In fact in this case electricity behaves as if it possessed inertia.
In a paper published in the ' Philosophical Magazine,' April 1881, I
have shown that the kinetic energy of a charged sphere of radius a and
mass m moving at a velocity q
where /z is the magnetic permeability of the surrounding dielectric and
e the charge on the sphere. If there are two spheres in the field, then
I have shown in the same paper that the kinetic energy
— 2^2 +TT ~r 2 + 2'" 1 + T5 — T 2 + 3~^ 22 COS f,
a a sst
where corresponding quantities for the two spheres are denoted by plain
and accented letters. We see from this expression that the forces
between the spheres are exactly the same as those given by Clausius'
formulae. It would not, however, be legitimate to go and develope the
laws of electrodynamics from this result in the way that Clausius does,
as Clausius' conception of an electric current does not accord with that
of the displacement theory. We may remark that in this case the part
of the kinetic energy due to the electrification is always positive.
On theories which are based on dynamical considerations, hut which
neglect the action of the dielectric.
F, E. Neumann ' was the first to develope a theory founded on the
principles of the Conservation of Energy. His theory was based upon
the assumption that two elements of circuit ds, Js', traversed by currents
I, i' possess an amount of energy equal to
a^ijLss^ dsds',
r
' ' Die mathematischen Gesetze der inducirten electrischen Strome,' Schriften der
Berliner Academie der Wissemch., 1845.
ON ELECrBICAL THEOBIES. 115
where A is a constant which depends upon the unit of current, r is the
distance between the elements, and e the angle between their directions.
F. E. Neumann showed that this assumption leads to the same law of
force between two closed circuits as that given by Ampere, and also ex
plained by means of it the induction of electric currents, v. Helmholtz ^
has investigated the most general expression for the energy possessed by
two elements of current which is consistent with the condition that the
force between two closed circuits should be the same as that given by
Ampere's theory. We shall consider this theory in detail, as it includes
all theories of this class, and we shall wish to refer to it when we come
to discuss the relative merits of the various theories, v. Helmholtz
hegins by showing that the most general expression for the energy of two
elements of circuit consistent with Ampere's laws for closed circuits is
1 A^L^ 1(1 ^ ^) (508 £ + {11) cos e cos &} ds ds',
where 9 and 6' are respectively the angles ds and ds' make with the line
joining the elements, ^ is a constant, and the other symbols have the same
meaning as before.
Let us call this quantity T ; then we know thatT denotes the existence
•of a force dT/dr or
 i ^—^ {(1 + ^) cos £ + (1  h) cos d cos 8'} ds ds'
along r, and a force — dT/rdd at right angles to r in the plane of ds and
r, and in such a direction that it tends to diminish d ; this force equals
i ^Ll^^lk) fsin fl cos 6' + cos sin d' —^ ;
rand since
dd' '
^=cos ,,
where rj is the angle between the plane containing r and ds and that
containing r and ds', the transverse force
A^ I i'
= ^ 2 — 0~^) W'^ " COS 0' + cos 9 sin 6' cos r)] .
We see that these'forces will coincide with those assumed in Korte
weg's theory if the quantities a, I, c, d, which occur in that theory, have
the following values :
o= — A'
b= 1(1 + ^^ A»
d=^(lk)A^.
So that whatever ^be the value of /,, these quantities", satisfy the con
•dition
2a + b + c2d=  .3A2.
' Crelle, Ixxii, p. 57; Gesammeltc Werke, vol. i. p. 645.
IS
116 REPORT — 1885.
According to Stefan, it is necessary if two circuits have a potential
that
2a+b¥ c2d=0.
But Stefan did not consider the couple exerted by one element of
circuit on another. The couples acting on the element els' will be as
follows. There will be a couple tending to increase 6', i.e. a couple
whose axis is at right angles to both ds' and r, equal to dT/dd', i.e. to
1 4liL {(1 + Jc) sin cos & cos »,2 cos 9 sin d'},
and another couple tending to increase v, i.e. a couple whose axis is along
the line joining the elements equal to dT jdr), i.e. to
1 A^
2
(l + Z;) sin 6 sin 0' sin >;■
r
"We see that these will agree with the couples in Korteweg's theory of
r ' r r
Let us return to the consideration of the energy of the circuits, and
suppose that, instead of currents flowing along linear circuits, we have a
distribution of them throughout space. If n, v, w be the currents in
the element dx, dy, dz, then the part of the energy contributed by this
element will be
 A2 {[]u+Yv+Ww}'dx dy dz,
where
d^ dr) d^,
with symmetrical expressions for V and W, where
r^ = (x  ly + (1/  vT + (z  zy.
We may write the expressions for TJ, V, W in the form
v=i(iA)^ + jj^d^d,dc
where4'= III {% +   + ^'^ ) ^'' ^"^ "^^ ■
If u, V, IV are the components of the ordinary conduction current, e the
volume density of the free electricity, then
du dv dw de \
dx dy dz dt'
and if 1, m, n be the direction cosines of the normal to a surface at which
ON ELECTKICAL THEOBIES. 117
the currents become discontinuous, a the surface density of the electricity
on this surface, then
I (u—u^) + m (v—v^) + n (lu—xu^) f __ = 0.
(XiJ/
Remembering these equations, 4/ may be transformed into
\\\ r —dx dy dz + \\ r —  ds :
JJJ dt ^ ^ ]] dt '
■or if (j> denote the electrostatic potential of the free electricity, we see
\h ^ — ~ dx dy dz.
^ 27r JJJ r dt ^
Substituting this value of ^ we find
dxdt
ay at
We also see that
^^W = (lk)^4.7riv.
dzdt
dx dy dz dt
In order to get the equations connecting the electromotive force with the
variation of the electrodynamic potential, Neumann made use of Lenz's
law, and assumed that, since by that law the electromotive force tending
to"'increase the current in an element of circuit moving with a velocity
■w in the direction s would be of the same sign as
— Xzy,
where X is the force along s on the element per unit of length per unit
of current flowing through it, it was actually equal to this quantity
multiplied by a constant c, i.e. to
— cKw;
but if Ti ds be the energy of the element of current whose length is
d&, and current strength i,
X=^'^
and w=^ = ;
dt
so that the electromotive force per unit of length of the element
__ ^ ds
ds dt
_ (IT
~'dT
118 REPORT— 1885.
V. Helmholtz has shown that it follows from the principle of the Conser
vation of Energy that if the energy in the elements dx, dy, dz, traversed
by currents u, v, w, be
A2 (TJu+Yv + Ww) dxdydz,
then the components of the electromotive force parallel to the axes x, y, z
respectively, due to the variation in the electrodynamic potential, will be
A^^, A2'!Y, A^^^;
dt ' dt ' dt
the free electricity produces an electromotive force whose components are
d<f) d<j> d<ji
daj' dy' dz'
so that the total electromotive force parallel to x, y, z
dx dt
Now if a be the specific resistance of the conductor, mi equals the elec
tromotive force parallel to the axis of .v, so that
dx dt
so that by the preceding equations
47rl ^ \lxdtl dx dt*
with similar equations for V, W. The quantities U, V, W and their
first difierential coefBcients with respect to x, y, z are continuous, and
these equations enable us to find them if we know the value of ^,.
the potential of the free electricity. Helmholtz shows that the whole
energy in the field due to the currents may be written
so that if h be negative, this expression may become negative, and in'
that case the equilibrium would be unstable ; hence we conclude that
only those theories are tenable for which /.■ is positive.
The equations written above are those which hold in a conductor,,
in an insulator the equations are
r2
■ ^=(i"> Wit
dz dt
v. Helmholtz shows that in the conductor the electrostatic potential <^ 1
satisfies the equation
ON ELECTRICAL THEORIES. 119
SO that if tlie conductor has an infinitely small resistance, the equation
becomes
v»2 A — A 2?.
V^(t> = A.Vc'^
This represents a wave motion, the velocity of propagation of which is
lA^yk. If 1c, as in ISTeumann's theory, be equal to unity, then the
velocity of propagation is 1 /A, and from the value of A, found from
experiments on the force between circuits conveying currents, this is
nearly equal to the velocity of propagation of light. Thus, according to
Neumann's theory, in a perfect conductor an electrostatic disturbance is
propagated with the velocity of light. In an insulator satisfies the
equation
and this represents a motion propagated with an infinite velocity, and
thus, according to this theory, an electrostatic disturbance is propagated
with an infinite velocity in a perfect nonconductor. In an imperfectly
conducting substance the velocity of propagation of a wave motion would
depend upon the length of the wave.
Let us now go on to consider, what, according to this theory, are the
forces acting on an element of circuit conveying a current. Let us suppose
that the element ds forms an element of a circuit through which a current
t is flowing ; then the energy of the circuit will be
J I as as ds J
In order to find the force parallel to x, let us suppose that each element
of the circuit receives an arbitrary displacement x, parallel to the axis of
X ; then the alteration in the energy will be
^,r f'i^'^+'^du^dWdzi^^^^^^.r^,^^^^ ■
J L dx ds ax US x as J } ds
Integrating the second term by parts, we see that it may be written
TA^ TJ^a;1 — A^ f t / ^U (?a; rfU */ c^ W cZs "1 ,
] \ dx ds dy ds dz ds J '
Substituting this value for the second term, we see that the alteration in
the energy,
= C'»3 + f • { I (^Jf ) S (f  f ) }  * ^
hence we see by the Conservation of Energy that there is a force on each
element of current parallel to the axis of <c, equal to
^ / dy /dV _dV\ _dz fdJJ _dW\ T . j
l ds\dx dy J ds\dz dx J J '
and by symmetry forces parallel to y and z equal respectively to
Jdz/'dW_dY\ dxfdY dV\ 1 ^2.
Ldsvd;/ dz J ds\dx dyj j
J^fd^_dW\_clyfdW_dV\l.^
\ ds\dz dx J ds\ dy dz) J
120 EEPORT — 1885.
so that the resultant of these forces is at right angles to the element. In
addition to these forces there are other forces at places where the quantity
lU is discontinuous, or, since U is continuous, at places where i is discon
tinuous, whose components parallel to the axes of x, y, z, are respectively
A2[J?(, A2V^\, A^W^i;
bnt II equals de/dt, the rate at which the free electricity is increasing
at the place, so that we have at any place where the free electricity is
changing a force whose components are
dt
A2V
dt'
A^W^^
dt
We saw before that the force acting on the circuit per unit length is
at right angles at each point to the element of circuit at that point, so
that, unless a circuit includes places at which the quantity of free electri
city is changing, the circuit will behave as if it were acted on by forces
which were everywhere normal to the elements on which they act. In
the experiments which have been made to test whether the force on the
element is at right angles to it, there have been no points where the free
electricity is changing, so that these experiments do not contradict Neu
mann's theory, although, according to it, the force on an isolated element
is not necessarily at right angles to that element, for in addition to the forces
normal to the element we have forces equal to A^UcZe jdt, A?Yde j dt, A^W de/dt
parallel to x, y, z respectively, acting at the ends, the resultant of these
two forces is a force whose components parallel to the axes of x, y, z are
respectively
A^dedUds
dt ds
A^dedVds
dt ds
A^dedWds
dt ds
and as these forces are not necessarily at right angles to the element, the
resultant force is not necessarily so ; the eifect of these forces could not,
however, be detected unless there was a discontinuity in the current.
V. Helmholtz in the memoir ' which we have already quoted shows
that, according to his extension of F. E. Neumann's theory, the forces
between two elements of circuit ds and ds' may be looked upon as made
up of —
(1) A iepulsive force on ds due to an end of ds', equal (per unit
length) to
. , de'l dr
atrds
" Ueber die Theorie der EJelitrodynaviih, dritte Abhandlung, Crelle, Ixxviii. pp. 273,
324, 1874; Gesammelte Werke,^. 723.
ON ELECTRICAL THEORIES. 121
(2) A repulsive force on ds due to ds', equal per unit length to
^ < 2 cos (tZif ds') — 3 cos {r ds) cos (r ds') > ;
(3) A repulsion between the ends of ds and ds', equal to
 ^(1 + *) ^' If ^
(4) A repulsion on ds', due to an end of ds equal per unit length to
— A^t'^^.
dt r ds
The second of these is the only one considered in Ampere's theory. We
must remember in calculating these forces that each element has two
ends.
Let us now go on to find the couples acting at each point of the
circuit. If the tangent to the circuit makes an angle with the axis of z,
and the plane containing the tangent and the axis of z an angle f with
the plane of xz, then we may write
^ = sin cos 0,
ds
^ = sin 6 sin d>,
as '
dz a
— = cos 0,
ds
so that with the same notation as before the energy equals
A^f. ru^+v$ + wtV>
J V 'Is ds dsj
= A^ £ (U sin e cos ^ + V sin sin (/) + W cos 0) ds,
so that if ^ increase by c^, the alteration in the energy equals
A^ I I ( — U sin 9 sin ^ + V sin cos ^) h<p ds,
so that the couple tending to increase (j>, i.e. the couple whose axis is
parallel to the axis of z, equals
A^ I (V sin d cos <^ — U sin sin <^)
per unit length of current ; this may be written
A^ ("vt  U^V
\ ds dsJ
hence the couples parallel to the axes of y and x are by symmetry re
spectively
I ds ds J '
A^i Iw'^V^\.
I ds ds J
122 REPOET — 1885.
Tlae axis of the resultant couple is perpendicular to the element and to
the vector whose components are U, V, W.
In another paper • v. Helmholtz discusses the force acting per unit of
volume on a conductor traversed by electric currents ; he shows that,
according to the potential theory, if u, v, w are the components of current
through an element clx cly dz, and X, Y, Z the components of the force
acting on this element of volume per unit of volume, then
V A,r C^^ ^U\ AiW cZU\ ^del
^=^'bUdy) + ^[^.dJ + ^dij
^ . r fdXJ dV\ /dW dy\ „ del
rr . , r /"'^U c?W\ (dY dW\ ^ del
He then discusses the application of the potential law to sliding contacts,
that is, contacts such as those made by a wire dipping into mercury ; in
the derivation of the forces from the potential law it is assumed that the
displacements are continuous, and it might be objected that we have no
right to apply the law in this case as the motion of the wire and the
mercury seems at first sight discontinuous, v. Helmholtz, however,
points out that, as the wire carries the mercury with it as it moves, the
motion is not really discontinuous and that Neumann's law is applicable.
The question of sliding contacts comes prominently forward when we
compare the various theories ; we shall return to it again in this con
nection.
V. Helmholtz also in this paper investigates the electromotive foi'ces
acting on a conductor in motion ; he shows that if the components of the
velocity of the conductor at any point are a, /3, y, then P, Q, R, the com
ponents of the electromotive force, are given by the equatioit
„  /dU dV\ /dXJ dW\ d ^^^ ^^ ^ ^
with similar equations for Q and R.
He also investigates the difference between the results of Ampere's
and Neumann's theory for the E.M.F. due to induction. The results are
complicated ; for practical purposes it is sufficient to notice that when
there is a mechanical force tending to make the body move in a certain
direction, there must be an E.M.F. when the body moves in that
direction.
C. Neumann^s Theory.
C. Neumann assumes that the electric potential energy is propagated
with a finite velocity, and that if two electrified bodies are in motion, the
mutual potential energy is not ee'/r, where r is the distance between them,
but ee'/r', where r' is the distance between them at a time t before,
where t is the time taken by the potential to travel from the one body to
the other.
The energy considered in C Neumann's theory is a kind of energy
quite different from any that we have experience of; it is not poten
' Ueher die Theorie der Elehtrodynamik, Crelle, Ixxviii. pp. 273324, 1874 ;
Gesammelte Werke, vol. ii. p. 703.
ON ELECTRICAL THEORIES. 123
tial energy, because that at any time depends only on the position of the
system at that time ; it is not kinetic, because that depends only on the
position and velocity of the system at the time under consideration,
■whilst Neumann's energy depends on the velocity and position of the
system at some previous time. In spite of ail this, however, Neumann
applies the ordinary dynamical processes to this energy just as if it were
kinetic or potential ; and in this way arrives at the same expression as
Weber for the force between two moving electrified bodies. The rest of
the theory is the same as Weber's, except that Neumann's assumption
about the nature of a current is different from Weber's. According to
Weber, an electric current consists of equal quantities of positive and
negative electricity, moving with equal velocities in opposite directions.
According to Neumann, the positive electricity alone can move, the nega
tive being attached to the molecules of the conductor. Riecke and Clausius
have shown that with this assumption and Weber's law a steady current
must exert a force upon a particle at rest and charged with electricity, and
must in consequence produce an irregular distribution of electricity over
any conductor in its neighbourhood.
Theories tohicli are founded on dynamical considerations and which take
into account the action of the dielectric.
In the theories we have hitherto considered, the influence of the
medium which exists between the currents has been left altogether out of
account. In the theories which we shall now proceed to discuss, the in
fluence of this medium is taken into consideration. This is, perhaps, the
most important step that has ever been made in the theory of electricity,
though from a practical point of view it is comparatively of little import
ance ; in fact, for practical purposes almost any one of the preceding
theories will satisfy every requirement.
Faraday was the first to look upon the dielectric as an important
agent in electrical phenomena ; he was led to this by his desire to get rid,
as far as possible, of the idea of action at a distance, which was so pre
valent in his time, but to which his researches have given the deathblow.
In his ' Experimental Researches,' § 1164, speaking of electrostatic in
duction, he says, ' I was led to suspect that common induction itself
was in all cases an action of contiguous particles, and that electrical
action at a distance (i.e. ordinary inductive action) never occurred except
through the influence of surrounding matter.' And later on he gives his
views as to the nature of the efiect in the medium; in § 1298 of the
' Researches ' he says, ' Induction appears to consist in a certain,
polarised state of the particles into which they are thrown by the electri
fied body sustaining the action, the particles assuming positive and
negfitive points or parts, which are symmetrically arranged with respect
to each other and the inducting surfaces or particles. This state must
be a forced one, for it is originated and sustained only by force, and
sinks to the normal or quiescent state when that force is removed. It
can be continued only in insulators by the same portion of electricity,
beca.use they only can retain this state of the particles.' He gives an ex
perimental illustration of his view in § 1350. He says, ' As an illustration
of the condition of the polarised particles in a dielectric under induction
I may describe an experiment. Put in a glass vessel some clear rectified
124 EEPOET— 1885.
oil of turpentine, and introduce two wires passing tlirough glass tubes,
when they coincide with the surface of the fluid and terminating in balls
or points. Cut some very clean dry white silk into small particles, and
put these also into the liquid ; then electrify one of the wii'es by an
ordinary machine and discharge by the other. The silk will immediately
gather from all parts of the liquid and form a band of particles reaching
from wire to wire, and if touched by a glass rod will show considerable
tenacity ; yet the moment the supply of electricity ceases the band will
fall away and disappear by the dispersion of its parts. The conduction
by the silk is in this case very small, and after the best examination I
could give to the effects, the impression on my mind is that the adhesion
of the whole is due to the polarity which each filament acquires, exactly
as the particles of iron between the poles of a horseshoe magnet are held
together in one mass by a similar disposition of forces. The particles of
Bilk therefore represent to me the condition of the molecules of the
dielectric itself, which I assume to be polar, just as that of the silk is.
In all cases of conductive discharge the contiguous polarised particles of
the body are able to effect a neutrahsation of their forces with greater or
less facility, as the silk does also in a very slight degree. Further we are
not able to carry the parallel, except in imagination ; but if we could
divide each particle of silk into two halves, and let each half travel until
it met and united with the next half in an opposite state, it would then
exert its carrying power (1307), and so far represent electrolytic
discharge.'
And it is not only in statical electricity that Faraday recognised the
importance of the dielectric. When he is discussing his discovery of the
induction of currents, which he ascribes to the assumption of what he
called the electrotouic state by the body in which induced currents are
developed, he says, § 73, ' It may even exist in nonconductors,' that is,
that there is an electromotive force acting on the surrounding dielectric
due to the variation in the primary current. Again, in § 1661, he says,
* Now though we perceive the effects only in that portion of matter which,
being in the neighbourhood, has conducting properties, yet hypotheti
cally it is probable that the nonconducting matter has also its relations
to, and is affected by, the disturbing causes, though we have not yet dis
covered them. Again and again the relation of conductors and non
conductors has been shown to be one, not of opposition in kind, but only
in degree (1334, 1603) ; and therefore for this, as well as for other
reasons, it is probable that what will affect a conductor will affect an
insulator also, producing, perhaps, what may deserve the term of the
electrotonic state (60, 24"2, 1114).' And though he was unable to detect
these effects experimentally, the following paragraph (1728) shows that
his belief in their existence was not shaken : ' But then it may be asked.
What is the relation of the projierties of insulating bodies, such as air,
sulphur, or lac, when they intervene in the line of magnetic action ?
The answer to this is at present merely conjectural. I have long thought
there must be a particular condition of such bodies, coi'responding to the
state which causes currents in metals and other conductors (26, 53, 191,
201, 213) ; and considering that the bodies are insulators, one could
expect that state to be one of tension. I have, by rotating nonconduct
ing bodies near magnetic poles, and poles near them, and also by causing
powerful electric currents to be suddenly formed and to cease around
and about insulators in various directions, endeavoured to make some
1
I
ON ELECTRICAL THEOraES. 125'
sncli state sensible, but have not succeeded. Nevertheless as any such
state must be of exceedingly low intensity, because of the feeble intensity
of the currents which are used to induce it, it may well be that the state
may exist, and may be discoverable by some more expert experimentalist,
though I have not been able to make it sensible.'
Maxwell was the first to express Faraday's ideas in mathematical
language. In his papers on ' Physical Lines of Force ' in the ' Philoso
phical Magazine ' for March, April, May, 1861, and January, February,
1862, he developes a theory of electricity according to which the eneroy
of the electromagnetic field resides in the dielectric as well as in the con
ductors ; later, in the ' Philosophical Transactions ' for 1865, he greatly
extended Faraday's ideas as well as put them into definite mathematical
language, and this without reference to any special theory of the mechan
ism which produces electrical phenomena. We shall devote some time to
discussing Maxwell's theory, as it is freer from serious objections than any
other, while at the same time it covers a much wider ground.
We shall begin by referring to Maxwell's view of the state of the
dielectric in the electric field. Maxwell supposes that the dielectric i&
changed, and perhaps the clearest way of describing this change is that
of Faraday in the extract already quoted. Maxwell's nomenclature as to
this change is a little unfortunate ; instead of speaking, like Faraday, of
the polarisation of the dielectric, he speaks of the change as consistino
of an electric displacement, which in isotropic media is in the direction oi
the electromotive force. Mathematically the two things are identical •
we may either say of a wire that it is negatively electrified at one end a'
and positively at the other end B, or else that there is a displacement of
positive electricity from A to B, so that there is an excess of positive
electricity at B and a deficiency at A. But though the words in a mathe
matical sense are identical, still the word displacement seems to connote
special qualities which limit the generality of the conception in an unde
sirable way ; the word displacement seems to imply motion in the direction
of displacement, while polarisation only implies that there is a vector
change of some kind in the dielectric. The condition of the dielectric is
quite analogous to the state of a piece of soft iron placed in a magnetic
field. The polarisation or displacement is in isotropic media in the direc
tion of the_ electromotive force and proportional to it, just as the magnetic
induction in isotropic media is in the direction of the mao'netic force and
proportional to it. It was this proportionality combined with the fact that
as soon as the electromotive force is removed the dielectric sprinos back,
as it were, to its original state, that led Maxwell to use the word dis
placement. He looked on the case as analogous to that of an elastic
solid, which springs back to its original position when the external force
is removed, and in which the displacement is proportional to the im
pressed force. To avoid any unnecessary definiteness we shall use the
term dielectric polarisation instead of electric displacement. Thus
according to this view the dielectric in the electric field is polarised.
This polarisation means change of structure of some kind, and to produce
this change of structure work is required. The energy in the polarised
dielectric will be greater than the energy when it was unpolarised, for if
the energy were less the dielectric would go into the polarised condition
of itself, without the application of any external forces.
It is rather difficult to see what is meant in Maxwell's theory by the
phrase ' quantity of electricity.' According to the old twofluid theory
126 BEPORT — 1885.
an electrified body was supposed to contain a certain quantity of some
thing called electricity, rules were pven for measuring this quantity,
and the phrase ' quantity of electricity ' meant something quite definite.
In Maxwell's theory, where everything is referred to the dielectric, the
meaning of the phrase is not so obvious. We can, however, arrive at
some idea of what is meant by the consideration of what are called ' tubes
of force.' Let us suppose at first that the dielectric is air. A line of
force is a line whose direction at any point coincides with the direction of
the electromotive force at that point, so that we may conceive the electric
•field to be filled with lines of force. If we consider the lines of force
passing through some small closed curve, they will form a tube, and such
a tube is called a tube of force ; and if the dimensions of the tube are such
that the product of the cross section at any point and the electromotive
force at that point is constant and equal to iir, the tube is called a unit
tube. We may thus conceive space to be filled with unit tubes of force.
Since the electromotive force inside a conductor vanishes these tubes will
end at the surface of a conductor. And the quantity of electricity on the
conductor will be equal to the excess of the number of lines of force which
leave the conductor over those which enter it. A tube is said to leave the
conductor when the direction of the electromotive force is along the normal
vdrawn outwards, and to enter it when the direction of the electromotive force
is along the normal drawn inwards. As the conductor moves about it may
be supposed to carry the tubes of force along with it, so that the number of
tubes which end on the conductor remains constant. This way of look
ino at electrification is quite satisfactory as long as we keep to one
dielectric air ; when we have to consider difi'erent dielectrics it requires
modification, because the electromotive force changes abruptly as we pass
from one dielectric into another, so that a tube which was a unit tube in
one dielectric is not so in another. It is easy, however, to extend the
definition of unit tubes so as to meet this difficulty ; for if the tubes pass
from one dielectric A into another B the ratio of the product of the cross
■section and electromotive force is constant for all the tubes and depends
only on the nature of the dielectrics ; this ratio is the ratio of the specific
inductive capacities in B and A. Air is taken as the standard dielectric,
and the specific inductive capacity of another dielectric A is the ratio of
the product of the electromotive force and cross section of a tube in air
to the product of the same quantities for the same tube in the dielectric
A. Thus if we amend our definition and say that a circuit tube is one
such that the product of the cross section, the electromotive force, and the
specific inductive capacity of the medium in which the cross section is
situated is equal to 4?r, then the quantity of electricity on a conductor is
equal to the excess of the number of unit tubes which leave the conductor
over the number of those which enter it. In this way we get an idea of
Vi^hat is meant by ' quantity of electricity ' in Maxwell's theory. Maxwell
accounts for the forces observed between electrified bodies by a system
of stresses in the dielectric separating them ; as, however, at present we
wish to compare Maxwell's theory with other theories which do not
touch upon this point, we shall discuss this part of the theory separately
later on and go on to discuss those points which are involved in all the
theories.
The next great point in Maxwell's theory is the development of
Faraday's remark that the electrotonic state may exist even in noncon
•ductors, i.e., that the dielectric surrounding a changing current is acted
I
I
ON ELECTRICAL THEOEIES. 127
•on by electromotive forces which polarise it. This statement is one as
to whose truth nobody seems to entertain any doubt, whilst the state
ment that changes in the dielectric polarisation produce effects analogous
to those produced by ordinary conduction currents is by no means so
universally received, and yet the one seems the necessary consequence of
the other. If we regard the whole electric field as a dynamical system,
and to fix our ideas consider an element a of the dielectric, and the cur
rent, which is supposed to vary, then, since a variation in the current
polarises a, i.e., produces a change in its structure, there must be
mechanism connecting the current with the element a ; but if this is so
then it follows from dynamical principles that a nonuniform variation
in the structure of rt must produce a change in the current — in other
words, that a change in the rate of change of the polarisation of a pro
duces an electromotive force on the current, i.e. that the change of polarisa
tion produces an effect analogous to that of an ordinary conduction
current. We may illustrate this by a purely dynamical example. Sup
pose we have a dynamical system defined by two coordinates p and q,
and let T be the kinetic energy of the system and V the potential energy ;
then by Lagrange's equation the force tending to increase q
=  ^+ cZT__cZ^ dT
dq dq dt dq'
Now if there is a force tending to alter q which depends upon the
acceleration of p, there must be a term in the kinetic energy of the
form
but if we apply Lagrange's equations to the p coordinates we see that
•this term implies the existence of a force tending to increase p equal to
lit ^^'
so that an acceleration of q will produce a force tending to alter p.
To make this applicable to the case of the current and the dielectric, we
have only to suppose that p represents the current, q the polarisation of
the dielectric. That a change in p produces a change in q is shown by
the fact that the dielectric is polarised when the current is changing, and
this shows that there must be a term of the form A.pq, in expression for
the kinetic energy ; from this it follows that a change in q, i.e., in the rate
of change of the polarisation, will produce an E.M.F. on the circuit. As
the variation of the dielectric polarisation produces the same effect as a
conduction current, we must in the case, when both conduction current
and alteration in the polarisation are present, look upon the true or effec
tive current as the sum of the conduction current and the change in the
polarisation.
The components/, g, h of the dielectric polarisation are defined by the
equation
/=^x 9=~Tr h=^Z,
4n 47r 4n
where K is the specific inductive capacity of the medium, X, Y, Z the
components of the electromotive force. If u, v, w are the components
of the effective current, p, q, r the components of the conduction
128 KEPOET — 1885.
current, then Maxwell in his paper on a ' Dynamical Theory of the
Electromagnetic Field,' ' Phil . Trans., 1885,' puts
Since ^ + 1^ + ':^r = _ ^
dx dy dz dt
, df . da dh
and jL + ^ + r= P^
ax ay dz
■where p is the volume density of the free electricity, we see that
du dv div p.
dx dy dz
If the values of the quantities in a medium A be denoting by putting
the suffix 1 to the symbols representing them, and those in another
dielectric B by putting the suffix 2, then if I, m, n are the direction
cosines of the normal from A to B, we have at the boundary of the two
media
^ (ihpi) + m (qiq^) + n (rira) = ^
^ (/i /2) + ''* (ui Oi) + '^ {K1h) = <^,
where (r is the surface density of the electi'icity ; thus
I (ui—u^) + 111 (V1—V2) + n (W1 — W2) =0;
so that u, V, iv satisfy the same equations as the components of the velocity
of an incompressible fluid.
This assumption about the magnitude of the effects produced by the
alteration in the dielectric polarisation makes the mathematics of the
theory as simple as possible. If Maxwell had merely assumed that the
alteration of the dielectric polarisation produces effects analogous to those
produced by ordinary conduction currents, and that the equivalent con
duction current was proportional to the rate of alteration of the dielectric
polarisation, then these equations would have been
, dY
"=^+"^'
^ dZ
so that in a homogeneous dielectric
du dv dw '''^ / 1 _ 4 """ "l
d^ ckf ih dt\ TJ'
Z(w,— 1*2) + m. {v^—v^) + n {w^—Wi) = y+a^
dT , dN, dlif
It ' dt ^ dt
where N is the component of the electromotive force normal to the
surface .
ON ELECTRICAL THEOEIES. 129
Maxwell's assumption is that a=K/47r, and this makes the equations
much simpler ; it is, however, important to remember that Maxwell's
theory of the dielectric involves the two assumptions—
1st. That alterations in the dielectric polarisation produce effects
analogous to those of ordinary conduction currents ;
2nd. That the magnitude of the equivalent conducting current
= d I — F V Idt, where F is the electromotive force at the point ; this is
equivalent to saying that all the currents are closed currents, and that
there is no discontinuity in them.
Maxwell developes his theory by means of the principle of the Con
servation of Energy.
Let us consider an electric field full of currents, whether ordinary
conduction currents or polarisation ones. Then this field may be looked
upon as a material system, and all the phenomena have to be explained as
the effects of the motion of this system ; a current must be looked upon
as a change in the structure of the system, and so capable of representa
tion by means of the differential coefficients of the coordinates fixing
the system ; we can thus represent the current at each point as the
differential coefficient of some generalised coonlinate fixing the system ;
the components u, v, w of the current passing through an element dx,
dy, dz may be looked upon as the rates of change of some generalised
coordinates ; we may write the energy as
if 1 1 (Fm + Gv + B.w}dx dy dz,
where F, G, H may be looked upon as momenta corresponding to
u, V, w. It remains to identify F, G, H with known quantities. Maxwell
does this by the aid of Faraday's result, that the electromotive force
round a circuit equals the rate of diminution of the number of lines of
force passing through it.
Let us consider a single linear circuit in which the current is i, or
say dqjdt, then the energy
= ^J^h^ + G^+B^\ds,
J at L ds ds ds J
where ds is an element of circuit ; but by Lagrange's equation the force
tending to increase q, i.e., the electromotive force in the circuit,
= ^{(F'^^+GiM+K^')ds;
dtj\ as ds ds)
so that ffF ^4 G'i^+H^V*
]\ ds ds ds)
equals the number of lines of force passing through the circuit ; but if d^
be an element of surface closing up the circuit, I, m, n the direction cosines
of the normal, then by Stokes' theorem
f(
F — + G^ + R—^ds
ds ds dsj
1885.
ll{'{^f)+(ff)'(rf)}^
E.
130 EEPOET — 1885.
but the number of lines of force passing through the circtiit
= I (JO' + ini + nc)dS,
■where a, h, c are the components of magnetic induction, so that
dy dz '
dz dx
^^dG_clF
dx dy
To connect a, h, c with the current, Maxwell makes use of the prin
ciple that the line integral of the magnetic force taken round any closed
curve equals the current flowing through the curve. This leads to the
equations —
. dy dl3
4;r«=— — — ,
ay dz
. da dy
dz ax
A dft da
dx dy
so that if /u be the coefficient of magnetic permeability,
. dc db
dy dz
and so on. Substituting the values of a, b, c, given above, we find
dx I dx dy dz i
with similar equations for G and H.
Now V. Helmholtz, in his paper ' Ueber die Bewegnngsgleichungen der
Elektricitat fiir ruhende leitende Korper ' (Crelle, Ixxii. p. 57 ; Gesam
melte Werke, ii. p. 545), has investigated the most general expressions
for F, Gr, H, consistent with the force between two closed circuits agree
ing with that indicated by Ampere's theory, and he finds that if the
circuits are closed circuits, as Maxwell assumes all circuits to be, then
dx dy dz
and therefore 477^^= — v ^F,
with similar equations for G and H. These equations are sufficient to
determine the quantities F, G, H.
Maxwell does not at once put dFldx + dG/dy + dH.ldz=0; he writes
for this quantity, and puts
X= \—dx dy dz.
Then F=JJ^da; dy dz+^;
ON ELECTRICAL THEORIES. 131
as, however, he subsequently puts J=0, we may at once simplify the
equation by making this assumption.
Since the kinetic energy equals
1 ( [ [ (Fu + Gv + mu) dx dij dz,
we see by Lagrange's equations that the electromotive force tending to
increase u
dt '
in addition to this there is the force arising from the electrostatic poten
tial (j), so that the total electromotive force parallel to the axis of x
^_dF_d<j>
dt dx
so that if (s be the specific resistance of the substance, K its specific induc
tive capacity, then
47r . dF d(^
''P=K^=dtTx'
'^ '"' ^'^dt Adt dxi 4:7r\dt^ dicdti '
tut we saw before that
47r/i!{= — V ^F ;
substituting for u this value, we see
^^F^^fdY d^l Jd^ d^^
<r I dt ^dx / ^"^^ 1 dt^ ^dx dtr
^ihus in the dielectric the equation becomes
^idt^^dxdtr
in the conductor
o \ dt dx i
The equation for the dielectric shows that it represents a wavemotion
propagated with the velocity 1/v/K^; the numerical value of this velocity
agrees very approximately witla the velocity of light, and this led Max
well to the theory that the changes in the structure of the dielectric
which take place when the dielectric is polarised are of the same nature
as those which constitute light. This theory, which is called the electro
magnetic theory of light, might almost as justly be called the mechanical
theory of dielectric polarisation. Earchhoff, in his paper ' Ueber die
Bewegung der Blectricitat in Drahten ' (Pogg. Ann., vol. c. 1857 j
Gesammelte Werke, p. 131), was the first to point out that some elec
trical actions are propagated with the velocity of light. In this paper he
considers the motion of electricity in wires whose diameters are small
compared with their length. There are three things which have to be con
sidered in this problem — (1) the selfinduction of the electric current, and
k2
132 REPORT— 1885.
if the medium be taken into account, that of the polarisation currents in
the dielectric. This selfinduction produces very much the same effect
as if the electric current possessed momentum— (2) the electrostatic action
of the free electricity which tends to bring things to a definite state, and
corresponds very much to the spring in a material system. Then, lastly,
there is the electrical resistance, which corresponds to fi'iction in an ordinary
system. We see from the analogy that if the resistance be small enough,
the electrical system will vibrate ; if, however, the resistance is large,
the electrical disturbance will be propagated in the same way as heat.
Kirchhoff in his paper considers the propagation of electrical disturbance
along a wire under various conditions : we shall only consider here one
of these cases ; that of an endless wire. In his solution Kirchhoff only
considers the selfinduction of the current flowing along the wire ; he
does not consider the effects in the surrounding dielectric. He shows
that if e be the quantity of electricity per unit length of the wire, and
e=X sin ns,
where s is the length of a portion of the wire measured from some fixed
point, then X satisfies the differential equation
cPX c^r dX c2 d''X
dt^ I6yl dt 2 ds^ '
where c is a quantity which occurs in Weber's theory, and is the velocity
with which two charged particles must move if the electrodynamic
attraction between them balances the electrostatic repulsion ;
r is the resistance of the wire in electrostatic measure ; y = log If a,
where I is the length of the wire and a the radius of its cross section.
The form of the solution of this equation depends on the magnitude of
If this quantity be large, the solution takes the form representing the
propagation of a wave along the wire with the velocity c/\/2. Weber's
researches show that this velocity is very nearly equal to the velocity of
light. If, however, the abovementioned quantity be small, then the
solution of the equation takes the same form as the formula which
expresses the conduction of heat along the wire. We must not, however,
take this to mean that the electric disturbance is propagated with an
infinite velocity, so that if we had an infinitely delicate electrometer at a
finite distance from the source of disturbance we could detect an electrifi
cation after an indefinitely short time, for it seems obvious that the
electrical resistance cannot increase the velocity of propagation any more
than the resistance of the air could increase the velocity of propagation of
a disturbance along a line of particles connected by an elastic string.
The conditions at the end help to determine the form of the solution, and
these cannot make themselves felt until the disturbance has reached it ;.
thus the heat form of solution probably only holds after a time from the
commencement of the disturbance greater than the time taken by light
to travel along the wire. If we take the case of a copper wire one square
centimetre in area, we shall find that the wave form of solution will hold
if the wire is not more than 100 miles in length, while the heat form
will correspond to wires which are much longer than this. Kirchhoff's
ON ELECTRICAL THEORIES. 133
solution only refers to the propagation of a disturbance in a conductor,
while Maxwell's refers to the propagation of such a disturbance in the
dielectric.
Maxwell considers the effect of the motion of the medium on the elec
tromotive force ; he shows that the electromotive force parallel to the
axis of X
where u, v, to are the components of the velocity of the medium conveying
electric action. Here \p is not the electrostatic potential merely; it is
equal, as Helmholtz has shown,' to the electrostatic potential plus the
term
Fu + Go + Hw.
We must remark here that ti, v, lo are the components of the velocity of
the medium conveying the electric action, i.e. the ether, and this need
not necessarily be the same as the velocity of the dielectric.
V. Helmholtz' s Dielectric Theory.
V. Helmholtz, in the paper ^ to which we have so often referred, con
siders the effect of the polarisation of the dielectric ; he supposes that
when an electromotive force X, parallel to the axis of «, acts on an
element of a dielectric, it puts it into such a state that it produces the
same effect as if there were electricity of surfacedensity x oii the face
dy dz of the element, and an equal quantity of electricity of the opposite
sign on the parallel face, x being given by the equation
the variations in the electromotive forces acting on the dielectric are
supposed to produce the same effect as ordinary conduction currents
whose components are x, g, ^, where x, g, 5 are the components of a
vector quantity which in isotropic media is parallel to the electromotive
force and equal to the product of e and the intensity of the force. This
agrees with Maxwell's assumption, provided
£ = K/47r,
where K is the specific inductive capacity of the dielectric. If <^ be the
electrostatic potential of the free electricity, ;// the potential due to the
polarisation of the dielectric, then Helmholtz shows that
+
A (l + 4;re)A(0l,/.) J=4tE,
where E is the volumedensity of the free electricity. The corresponding
equation in Maxwell's theory is of the same form, provided
lf 47r£ = K.
' Ueher die Theorie der Elehtrodynainih ; die eleJtirodynamisic'he Krdfte in
hewegteJi Leitern, Crelle, Ixxviii. p. 309 ; Gesammelte WerJte, ii. p. 745.
' Ueber die Theorie der EleMrodynamik, Crelle, Ixxii. p. 57; Gesammelte
WerTie, i. p. 644.
134 EEPOET — 1885.
This relation seems inconsistent with the previous one ; it may, how
ever, be reconciled with it in the following way : —
The potential dae to a quantity B of electricity at a point distant
r from it is proportional to
E
If £o be the value of e for air, the potential under the same circumstances
in air is proportional to
E
(l + 47reo)r'
if, then, we define unit potential as the potential at unit distance from
unit of electricity in air, the potential due to a quantity E in another
medium will be
r l + 47r£p 1 E
1 l + 47r£ J r'
We see that this is equivalent to increasing the unit of potential, and
therefore the unit electromotive force, l+47r£o times, so that if we use
the new unit the equations will be
^~l+47reo '
d r l+47r£ cl ,^1
= 47rE.
These will coincide with Maxwell's equation if we make £ and cq each
infinite and put K=£/fo.
Returning to Helmholtz's theory, if u, v, w are the components of the
total current
u=p + x,
where p, q, r are the components of the conduction current.
Helmholtz puts
du dv div dp
dx'^dy '^dz~~dt'
where p is the volumedensity of the free electricity, and if <t be the
surfacedensity of the free electricity at any point of a surface separating
two media, ^^l, Vi, w^; u^, v^, Wa the components of the current in the
two media, I, m, n the direction cosines of the nonnal to the surface
drawn from the first medium to the second, then according to v. Helm
holtz
According to Maxwell the corresponding equations are
du dv dw
dx dy dz '
I (ui—U2)+m (vi—Vo)+n (iOi—W2)=0.
ON ELECTBICAL THEORIES. 135
As it is in the difference between these equations that the difference
in the theory really lies, it will be instructive to look at them from
another point of view. We know of no way in which the quantity of free
electricity can be altered except by electricity being conveyed by con
duction cuxrents to the place where the alteration takes place. Assuming,
then, that the alteration in the density is caused by such currents
dp dq dr dp
l^'^~d~y'^Jz~~di'
I (PiP2)+m (2i22)+« (rir2)=^.
So that Helmholtz's equations taken in conjunction with these are
equivalent to the condition
dx dy dz '
Thus on Helmholtz's theory the dielectric currents behave like the
flow of an incompressible fluid, while on Maxwell's theory it is the total
current, which is the sum of the conduction currents and the dielectric
currents which behave in this way.
The equations we have arrived at for the dielectric currents seem
inconsistent with Helmholtz's definition of them ; for since
X=eX,
with similar equations for p and 3, and since in a medium at rest
dt dx'
dt~dy'
_dW_d(l,
dt ~dz'
where U, V, W are the components of the vector potential. If we consider
a surface separating two portions of the same dielectric and coated
with electricity whose surfacedensity is o, we have, since U, V, W are
not discontinuous on crossing the surface,
d r d<t> dm ddr\2
td<t) d(t> cZrf>"2
I ^ + m j+n y denotes the difference between the values
d(b d^ d<j>
of I J + WT" + n T~ on the two sides of the surface.
ci3J ciy dz
rU d<b d<t,f 1
e da
so that I {±^x^)^m {■Qi'Q^')^'^ (3i32)=l+4;re dt^
and so cannot vanish if the surfacedensity of the electricity changes];
136 REPORT — 1885.
thus Helmholtz's equation seems to be inconsistent with the principle
that the change in the quantity of free electricity is caused by conduction
currents. In the case above considered, Maxwell's equations lead to no
difficulty ; it does not follow, however, that Maxwell's assumption that
the total current behaves like the flow of an incompressible fluid is
absolutely necessary. We shall consider later on the differences which the
abandonment of this assumption will make in the theory.
We shall now go on to consider Helmholtz's equations and compare
them with the corresponding ones in Maxwell's theory.
The quantities U, V, W are given by equation of the form
U=J
^^'<t^\[
—d'E, dt) d^,
r
where h is the constant which we mentioned before as occurring in
Helmholtz's theory, and
where <f> is the electrostatic potential ; it follows from these equations
that
dJJ.dVdW , dd>
 — T — — r — ^j — Ic ~i.
ax ay dz dt
The corresponding equation in Maxwell's theory is
dx dy dz '
60 that these equations coincide if ^=0. We can see from the value of x
given on page 116 that, on Helmholtz's theory, this quantity would also
vanish, whatever be the value of k, if the total current behaved like the
flow of an incompressible fluid.
If a, /3, y are the components of the magnetic force, then on Helm
holtz's theory
ay dz Idtdx • J
dy
dz dx I dtdy J
dx dy idtdz J
where A is a quantity depending on the unit of current adopted, and is
such that the force between two parallel elements of currents at right
angles to the line joining them is
l^ijdsds',
where r is the distance between the elements, ij the current through them,
and ds ds' their lengths ; the corresponding equations on Maxwell's theory
are
dy_dl3 _,
dy dz
with similar equations for v and w.
ON ELECTRICAL THEORIES. 137
If X, n, V are the intensities of magnetisation, ■& tlie coefficient of
induced magnetisation, the equations satisfied by the components of the
dielectric and magnetic polarisation are of the type
__4^r^(l±M)__A2^+ r ^ _ (l + 4:r^)(l + 4:r0 "1 d_
(i+47r£o) (l + 47rSo) dfi \ k I dx
1 dx dy dz J
^ ~ (l + 47r£o) (1+477^0) ■^'
where eq ^^^ ^0 ^re the values of e and S for air.
These equations show that the dielectric and magnetic polarisations
are propagated by waves. For the dielectric polarisation longitudinal
waves are propagated with the velocity
1 ; (l+47rO (I+^tteq) (l + 47r5o) \l.
A I 47r£/j J
Transverse waves are propagated with the velocity
V2
+ 4;r£o) (l+47r^o)
47re (l+47r3)
Longitudinal waves of magnetic disturbances are propagated with
an infinite velocity, and traverse ones with the same velocity as the
transverse waves of dielectric polarisation. The electrostatic potential is
propagated with the velocity IjAs/k. In Maxwell's theory the corre
sponding equations are
where fx is the magnetic permeability and K the specific inductive capacity,
so that for both dielectric and magnetic polarisation the velocity of the
longitudinal wave is infinite, while the velocity of the transverse wave is
l/s/fiK. The velocity of propagation of the electrostatic potential is
infinite. If in Helmholtz's theory we put Z;:=0, •&o = 0, £/£o=K, while
both £ and £0 are infinite, we see that the results of his theory will in this
respect agree with Maxwell's.
Though in Maxwell's theory the velocity of propagation of the electro
static potential is infinite, and in Helmholtz's theory 1/A\/A;, the electro
motive force at a point, and consequently the dielectric polarisation, does
not travel with an infinite velocity in Maxwell's theory, or with the
velocity 1/A\/ A; in Helmholtz's. We can see the reason of this nacre
easily from Maxwell's theory, as the equations are simpler.
Using the notation of that theory, viz.,/, g, h, for the components of
the electric displacement, F, G, H for the components of the vector
potential, and ^ for the electrostatic potential, then in a dielectric the
equations are
4<rr . _ _ d¥ _ d(p
K^ ~ ~dt "dx
138 EEPORT— 1885.
477 df_ _ tPF _ d^
'K dt~ 'dF' dxdt'
but, since 47r/i ^= — v ^F,
we see that ±^v^F='^ + ^.
fi\L d.f' dxdt
Now, since v ^^ = 0, a particular solution of tWs differential equation
will be
dt dx
while the general solution will be the sum of this solution and the
general solution of
/iK dt^
The particular solution is propagated at the same rate as f, while the other
part of the solution represents a wave travelling with the velocity 1 / V^K.
Since the part of the solution which travels at an infinite rate satisfies
the equation
dt dx
or f= 0,
we see that the electromotive force due to the change in the vector
potential just balances the electrostatic electromotive force, so that until
the part of the vector potential which travels at the rate Ij s/fjiK comes
up the resultant electromotive force vanishes. This explains how the
electromotive force on Maxwell's theory travels at a different rate from
the potential, and a similar explanation will apply to Helmholtz's theory.
Helmholtz's equations for a conductor are
a^hc= (1 +47r^) 47rA2 f^^^ { V> + (1 + 4,r^/.) A^  }
where a is the specific resistance of the conductor ; on Maxwell's theory
the equations are
9 J du
These equations differ by terms involving the unknown constant h; but
V. Helmholtz's ' investigations on the motion of electricity along thin
conducting wires show that there is not much hope of distinguishing be
tween the theories by experiments on conductors. We have seen that
we can make certain equations which occur in Helmholtz's theory
coincide with the corresponding ones in Maxwell's by giving par
ticular values to certain constants. The difference in Helmholtz's and
Maxwell's views as to the continuity of the currents is too serious to let
us expect that we should ever get a complete agreement between the
' Zfeher die Benegvngsgleichxmgen der Elehtricitdt fiir ruheiide leitende Korper.
Gesammelte Werke, vol. i. p. 603.
ON ELECTRICAL THEOKIES. 139
theories ; and, in fact, make as many assumptions about the constants as
we may, there are still differences between the theories.
In order to get as general a theory of these dielectric currents as
possible, we shall investigate the consequences of assuming merely that
these currents are proportional to the rate of change of the electromotive
force, and write dielectric current^ r; (rate of change of the electromotive
force), where ?/ is a constant which for the present is left indeterminate;
In Maxwell's theory 7;=K/4n, where K is the specific inductive capacity
of the dielectric ; in Helmholtz's theory, i] is also proportional to the spe
cific inductive capacity. We shall denote the components of the dielec
tric currents by the symbols f, g, h; the components of the conduction
current by p, q, r, and the components of the total current by ii, v, w, so
that
u=p +/.
Let us put
du , dv dw p
dx dy dz '
I (ui—U2) + m (vi—V2) + n (wi—W2)=:^ ;
on Maxwell's theory I" and 2 are each zero.
If F, G, H are the components of the vector potential, then by
V. Helmholtz's investigation of the most general expression possible for
these quantities consistent with the condition that the forces between
closed circuits should agree with those given by Ampere's laws,
• ¥ = i(lk)^+f.{{{'td^dnd^,
with similar expressions for G and H, where Jc is a constant and
Transforming this expression we see, using the same notation as before,
that
1/'= rfi{l («! — 1^2)+™ (yj— Vo)!^ (^1— ^^2)} ^^
= fLrS(iS {{ fir P d^ dr, di;,
where dS is an element of a surface at which there is discontinuity in
u, V, w.
Let us now consider the equations which hold in a perfectly insulating
dielectric.
The rate of change of the x component of the electromotive force in a
medium at rest
= _^ _ d^(p
dt^ dt dx*
where ^ is the electrostatic potential ; it also equals // rj, so that
f__d^F_ d^(t>
H dt'^ dt dx
140 BEPOET — 1885.
Since in this case there is no conduction current u =/, and the pre
ceding equation for F shows that
substituting for/
if  — 1 , + —  = Y, we get, by dififerentiating this expression,
ax ay az ^ <=> •'
with regard to x and the corresponding equations for G and H with
regard to y and z respectively, and adding
v=^x  i (1^) vV = 4x,;xA^X + I V^^ } .
Now, as the dielectric is a perfect insulator, there are no conduction
currents, so that the density of the free electricity remains constant,
and therefore
From the expression for yp we see that
Substituting this value of v^J' in the equation for x, we get
which represents the propagation of a normal wave with the velocity
1/ V^Trrjk.
The transverse wave is propagated with the velocity l/v4rr)7/j, so
that if the view that light consists of electric or magnetic disturbances be
correct, since experiment shows that this velocity is very nearly equal to
l/'^Kfj., we must have 47rj; = K or ?j = K/47r, which is Maxwell's theory.
So that if we assume that light is_an electric phenomenon, then in those
mediain which its velocity = 1/n//uK Maxwell's theory that the electric
cui'rents flow like an incompressible fluid must be true.
If a, /3, y are the components of the magnetic force, then, since
4
F = 1 (1  z;) ii + Mi'i m dr, di;,
we see from Ampere's formula for the magnetic force due to a circuit
that
^^dH_dG _ dY
dy dz dz '
ON KLECTRICAL THEOKIES. 141
where V is the magnetic potential due to the magnetism in the field both
permanent and induced. From these equations we get
I dy dx j dz\. d.v dy dz J
= _ 4;r,,i«+ ^ i (1 _ /,) V^v^  x}
instead of the equation
da dS .
— — = — 4!Trw.
ay dx
We have been obliged to introduce another assumptionliere, viz., that
the magnetic force due to an element of current is given by Ampere's
expression.
We could not assume Maxwell's way of connecting currents with
magnetic force, viz. that the total current flowing through any closed
curve is equal to the line integral of the magnetic force round the curve,
for the result can only be true when the currents flow like an incom'
pressible fluid.
Let us now go on to consider the force acting on the medium convey
ing the current.
If we consider a continuous distribution of currents, the kinetic
energy
— 2
i i (F2i + Qv + B.w) dx dy dz.
If we derive the force parallel to x by the variation of the energy in
the usual way we find, just as in Helmholtz's paper, • that the force
parallel to x
I \dx dy) \dx dz) \dx dy^dljr
or with our notation
= V <
\ dx dy J \ dx dz J '
and that on any surface where there is a discontinuity in the values of
u, V, w there is a force equal per unit of area to
F [I («i — u^) + m (i^i — v^) + n (w, — w^)}
or F2.
In the same paper it is shown that it follows from the principle of the
Conservation of Energy that the force exerted by a distribution of cur
rents equals the force given by Ampere's expression along with a force
at the point ^r)l^ whose component parallel to the axis of x equals
\\\ (S + I ^ 1^) ^ (^' {^^) + ^' (y  v)+w' (zOyxdydz
■* J J V ^^' ~ "^'^ ■*■ '" ^^' ~ "^2) + '^ (^1  ^i) ] ^^^ G<'' (aJ 
> Die eleUrodi/namischen Kr'dfte in hewegten Lcitern, Crelle, Ixxviii. p. 298
1874, or Gesammelte Werke, vol. i. p. 733.
142 itEPOET— 1885.
or with our notation
' "^^ [^1'' {xD + v' (y  n) + w'(z O) ^^ dy d^
+ W"" ^T '(^^' («=  + ^' (y v) + w' (z o) ds,
where u', v', w' are the components of the current at the point ^ rj ^;
so that in addition to Ampere's forces we have additional forces
wherever P and S have finite values. From the above expressions we see
that any element where P has a finite value exerts a repulsive force equal
per unit of volume to
— ^ cos 6,
r
tending from the element ; where r is the distance of the element from
the point at which the force is reckoned, i the intensity of the current at
this point, and 6 the angle between the direction of the current and r.
Any element of surface where S has a finite value exerts a repulsive
force equal per unit of surface to
V
~' i cos y,
r
where the notation is the same as before. Of course none of these forces
exist in Maxwell's theory. They could be most easily detected in cases
where the part of the forces given by Ampere's theory vanishes as it
would for the case of an endless solenoid. In this case, though the
Amperian forces vanish, the forces due to the discontinuity in the current
do not, so that if the endless solenoid were to move under the action of
external currents it would denote the existence of discontinuity in the
current. An experiment of this kind has been made by Schiller ; we
shall discuss the results of it later.
To sum up, the differences between the most general theory which
takes into account the action of the dielectric, and Maxwell's, are —
1. The existence of a normal wave in the general theory, but not in
Maxwell's.
2. The difference in the velocity of propagation of the transverse
wave.
3. The difference in the relation between electric currents and mag
netic force.
4. The forces which arise from discontinuity in the currents.
The Experimental Evidence as to tlie Truth of the various Theories.
The theories we have considered may be divided into two great classes,
according as they do or do not take into account the action of the dielec
tric surrounding the various conductors in the field. The first thing,
therefore, that we have to do is to see whether experiment throws any
light on this point.
When a dielectric is in an electric field it experiences a change in its
structure ; this is rendered evident by the alterations in its volume and
elasticity observed by Quincke, by the change in its optical properties
\
ON ELECTKICAL THEORIES 143
observed by Kerr, and also by the fracture of the dielectric when the
field is made sufiBciently intense. So that whenever an electromotive force
acts on a dielectric it produces a change in its structure which we shall
always speak of as polarisation. This, strictly speaking, has only been
directly proved for electromotive forces produced by charges of statical
electricity ; but, unless we are prepared to say that the electromotive
force due to statical electricity is in some way different from that due to
a changing current, we must admit that when an electromotive force of
the latter kind acts on a dielectric it polarises it. And we are not with
out experimental evidence that the electromotive force due to variations
in the vector potential does produce some of the effects of the electromo
tive force due to a charge of statical electricity. Rowland's experi
ments have shown that a moving electrified body will set a magnet
placed near to it in motion. It follows from this, by dynamical prin
ciples, that if we have the charged body initially at rest and move the
magnet it will, if no other forces act upon it, be set in motion ; so that
in this case there is an electromotive force due to the motion of the
magnet, i.e., the variation in the vector potential produces the same
effect on the electrified body as the electromotive force due to a charge of
statical electricity. For this reason we shall suppose that the electro
motive force due to the variation in the vector potential always produces
effects on a dielectric on which it acts of the same type as those which
have been observed to arise from the action of an electromotive force due
to a charge of statical electricity.
Let us now consider a magnet surrounded by a dielectric. If we set
the magnet in motion, we produce an electromotive force which polarises
the dielectric. Let us, to fix our ideas, consider an element of the dielec
tric and the magnet. When the magnet moves it polarises the dielectric ;
it follows from dynamical principles (an extension of the principle of
action and reaction),' that if the polarisation of the dielectric be
altered, the magnet will move, so that a change in the polarisation of a
dielectric produces a magnetic force.
Again, let us instead of the magnet consider a coil of wire conveying
a current. A change in the rate of flow of the current produces a
change in the polarisation of the dielectric ; it follows that a change in
the rate of change of the polarisation of the dielectric will produce a
change in the current, i.e., will produce an electromotive force.
It follows too, from dynamical principles, that as the change in the
polarisation of an element of the dielectric due to the change in the
current depends on the distance of the element from the current, there
must be a force between the current and the element when the polari
sation of the latter is changing. Thus we see that a change in the
polarisation of the dielectric must produce all the effects of an ordinary
conduction current, so that it is only absolutely necessary to consider
how the experimental evidence affects those theories which take the
action of the dielectric into account. As, however, the experiments
which have been made are few in number, and are all concerned with
interesting points, we shall consider them in their relation to all the
theories, and not only to those which take the dielectric into account.
' See a paper by the author of this report ' On some Applications of Dynamical
Principles to Physical Phenomena,' P/dl. Trans., 1885.
144 EEPORT — 1885.
Schiller's Experiments.
The first experiment whicli we shall discuss is oue made by Schiller^
and described by him in Poggendorf s Annalen, vol. clix. pp. 456, 537 j
it was intended to test the potential theories of Neumann and Helm
holtz. We saw that, according to these theories, in an unclosed circuit
there are, in addition to the forces due to the elements of current, and
which are expressed by Ampere's law, forces arising from the discon
tinuity of the currents at the ends of the circuit. If we have an end of a
circuit where the current stops, and the electricity accumulates at the
rate dejdt, it will exert on an element of current of length ds traversed
by a current of intensity i a force tending to the end and equal to
i 2 • 7 de cos Q
* * 'Jt ^r
where is the angle between the element of current and the radius drawn
to it from the end. If we calculate from this expression the couple pro
duced by an end on an endless solenoid, or on what is practically the
same thing, a ring magnet, we shall find that the couple tending to turn
the ring about an axis in its own place will not vanish, while the couple
arising from the forces given by Ampere's law will. Thus if the ring
rotates, as it should according to the potential theory, it must be from
the action of the end.
In Schiller's experiment the end of the current was the end of wire
connected with a Holtz machine. This was placed near to a ring magnet
which was suspended by a long cocoon fibre ; the magnet was protected
from electrostatic influences by being enclosed in a metal box connected
with the earth. Schiller determined the intensity of magnetisation of
the ring magnet and the quantity of electricity passing through the
point, and he calculated that if the potential theory were true, he ought
to get a deflection of the magnet of about 27 scale divisions, instead of
which there was no perceptible deflection.
This experiment shows conclusively that the potential theory is wrong
if we neglect altogether the action of the dielectric, and assume the cur
rent to stop at the end of the wire. If, however, we take the dielectric
into account, the experiment tells us nothing as to whether Maxwell's
theory or the more general one is true ; for since the current from the
Holtz machine is steady, as much electricity flows out from the end of
the wii'es as arrives there ; and thus there is really no discontinuity in
the current, the only difference being that before reaching the end the
current is flowing through copper and after passing it through air. The
condition of things at the end of the wire remains steady, and thus the
quantities which we denoted by P and 2 vanish.
The experiment might, however, be modified so as to be capable of
distinguishing between the theories which take the dielectric into account,
For suppose that, instead of letting the electricity escape through the
point, we never let the potential at the end of the wire get so high as to
allow the electricity to escape ; then if the wire is initially uncharged, the
condition at the end will be changing whilst the wire is charging up, and
thus 2 will have a finite value ; so that if the magnet were sufficiently
delicate and remained undeflected, whilst the point was surrounded by
dielectrics of all kinds, it would show that Maxwell's theory is correct.
I have calculated the effect which would be produced on Schiller's
ON ELECTRICAL THEORIES. 145
suspended magnet, and find that it is too small to be observed ; as, bow
ever, the time of charging up the wire will be very small compared with
the time of vibration of the magnet, the effect will be of the nature of an
impulse, so that in this case there will be considerable advantage in
having the moment of inertia of the suspended magnet small ; while,
as Schiller arranged the experiment, there was no such advantage, as the
thing expected was a steady deflection. Thus if the ring magnet were
retained it would be desirable to make the opening of it as small as pos
sible, retaining the same cross action. I think the arrangement could
be made sensitive enough to be deflected if the value of S were any
considerable fraction of the rate of increase of the electricity at the end
of the wire.
There is another way in which the continuity or discontinuity of the
current might be tested, and which might perhaps be more delicate than
the last. We saw on p. 141 that at any point of a current at which S
had a finite value the mechanical force on the element is not at right
angles to the element. In addition to the ordinary force at right angles
to the element, there is a force in the direction of the vector potential
equal in magnitude to the product of the values of the vector potential
and 2.
The existence of this force could be tested
by an arrangement of the following kind : —
AB and CD are light movable segments
of the same circle, having balls covered with
paraifin A, B, C, D fastened to their ends.
These segments are connected with a very light
framework which can rotate about an axis per
pendicular to the plane of the segments ; the
segments touch at their middle points contact,
pieces which are connected with a Holtz ma
chine. EP is the section of an electromagnet
concentric with AB and CD ; the whole is surrounded with a metal
cylinder to screen it from external electric influences. When a curi'ent
is passing through the electromagnet it produces a vector potential,
whose direction is at right angles to the radius from O, the centre of the
electromagnet perpendicular to its axis. Thus if 2 exists there will be a
couple tending to twist the system AB, CD about its axis, but if S exists
at all it will be when the electrical condition of the balls A, B, C, D is
changing, so that unless the currents are continuous we should expect the
system to rotate when the balls are being charged up. I have calculated
that the system might easily be made sensitive enough to be sensibly
deflected on charging or discharging, pi'ovided 2 is an appreciable fraction
of the rate of change of the surfacedensity of the electricity on the balls.
Schiller's Secojid Experiment.^
Schiller has made another experiment, which shows that Ampere's
theory fails for unclosed circuits. The first form of the experiment con
sisted in having a solenoid placed over a condenser one of whose plates
could rotate about a vertical axis coinciding with the axis of the solenoid.
One end of the solenoid was connected to one plate of the condenser and
the other end to the other plate. When the solenoid is connected to a
' Pogg. Ann., clix. p. 456; clx. p. 333.
1885. L
146 KEPOET— 1885.
battery the condenser will charge up and there will be radial currents of
electricity in the plates ; the current passing through the solenoid will
produce a magnetic force which will, if Ampere's theory be true, act on
the radial currents in the plate of the condenser and set it in rotation.
Schiller found that this effect was too small to be observed, so he modi
fied the experiment in the following way. Let us suppose that we have
the two plates of the condenser rigidly attached to their axis and placed
in a field symmetrical about its axis, in which the vertical component
of the magnetic force is not uniform. Then if a current be sent through
the upper plate, down through the axis, and out at the lower plate, the
couple tending to twist the lower plate will not be equal and opposite to
that tending to twist the upper one, as the magnetic force is not equal at
the two plates, and thus the condenser will be set in rotation. Con
versely, if the condenser be set in rotation in the magnetic field, and two
electrodes of a galvanometer be connected with its axis, then if Ampere's
theory be trne there will be an electromotive force acting round the
galvanometer circuit, which will produce a current, and this current
could be much more easily detected than the rotation in the first form of
the experiment. Schiller calculated the deflection which he ought to get
if Ampere's theory were true, and found that he could easily detect it if
it existed ; as he was not able to see any deflection, we must conclude
that Ampere's theory is not the true one.
It is easy to see that, according to the potential theory, there would
be no curreutin the galvanometer ; for, as everything is symmetrical about
the axis, the potential is not altered by the rotation. The following
calculation will show that, according to the dielectric theories, there should
be no current through the galvanometer.
For if a, b, c are the components of magnetic induction, F, G, H
those of the vector potential, X, Y, Z those of the electromotive force,
then
dt clt dx \ dt dt dt J
„ dz dx d ^ rj, dx p dy , ri clz\
^ = "^1 ' dt'dyV It^ ^ '^dt''^ dt]
i
Suppose the condenser is rotating with an angular velocity w about
the axis of Z ; then the E.M.F. arising from one plate is, if E, be its radius,
'^0
'(^S+«t)
Now F ^ h G I' = ..Re,
dt at
where is the component of the vector potential along the direction
of motion of a point on the circumference of the plate of the condenser.
But the line integral of the vector potential round any curve equals
the number of lines of magnetic force passing through it, so that, since
the field is symmetrical,
.R
27r cr dr = 27rRe.
ON ELECTRICAL THEORIES.
147
From this equation we see that the E.M.F. due to the rotation vanishes
for each plate, so that, according to this theory, there should be no current
through the galvanometer.
This experiment of Schiller shows that both Grassmann's and Clau
sius' theories must be wrong, as well as Ampere's and Korteweg's, for
we can easily see that they would make the disc rotate in the way in
which Schiller first tried the experiment, and if this were so, it follows
from dynamical principles that a current must be produced in the second
form of the experiment.
This would seem to be the case even if we take into account the cur
rents in the dielectric, unless we suppose that all the circuits are closed,
for if all the circuits are closed then the disc will not rotate, as all the
theories agree. If the circuits are not closed we may divide the currents
in the disc into two parts, one part being of such magnitude as to form
with the dielectric currents closed circuits ; then the forces on this part
and the dielectric will form a system in equilibrium ; and there remains
the other part of the currents, the action of the magnet on which ought to
set the disc in rotation. Taking Schiller's experiments together, we may
say that they show that the dielectric must be taken into account, and
that some form of the potential theory is the only one of the theories we
are considering which can give the expression for the forces due to a
distribution of currents.
Although these two experiments of Schiller's show that of the
theoi'ies we have discussed only the dielecti'ic ones can be retained, we
shall describe one or two more experiments which have been or could be
made to distinguish between the various theories. Clausius' and Grass
mann's theories lead to the same expression for the force between two
elements of current, so that these theories stand or fall together. Grass
mann in his paper ^ describes an experiment which would distinguish
between his theory and Ampere's, or, in fact, any other except Clausius'
which has ever been published.
Suppose that NS and SN" are two mag
nets whose north and south poles are de
noted by N and S respectively, and that
these magnets are fastened together by a
rod NS, the system being suspended by a
cocoon thread attached to the middle point
of NS. Let AB be an unclosed circuit, say
a wire joining the plates of a charged con
denser ; then, according to Grassmann's and
Clausius' theories, the system will rotate in
such a way that the sense of rotation is re
lated to a vertical line drawn downwards
like rotation and translation in a right
handed screw. According to every other theory it will rotate in the
opposite direction.
Another experiment has iDeen made by v. Helmhoitz,^ which shows
that the potential theory leads to wrong results unless the action of the
dielectric is taken into account, hh is a rotating conductor, to the ends
of which large condenser plates are attached, which, when in rotation,
come very near to the similar plates c, c. The plates h and c are segments
s
N
Pogg., Ixiv. 1, 1845.
WissensohaftlicJie Ahhandhmgen, vol.
783.
L2
148
EEPOKT — 1885.
of coaxial cylinders. lu v. Helmholtz's experiments bh was rotated
between the poles of a powerful electromagnet. The plates c, c were
connected with a commutator, which put them to earth when the rotating
piece was in the position A, and to the plates of a Kohlrausch condenser
when it was in the position B. Now suppose there is a difference of
potential between h and c ; suppose, for clearuess, that 6 is at a higher
potential than c, then when the rotating piece is in the position A the
positive electricity goes to earth, and the negative is left to go to the
Kohlrausch condenser, when the rotating piece gets to the position B.
The change in this condenser was measured by a quadrant electrometer.
V. Helmholtz found that the needle of the electrometer was deflected when
the piece hh was rotating. Since everything is symmetrical about the
axis of rotation, there would be no difference of potential between the
plates h and c, according to the potential law, if we neglect the action of
the dielectric. According to Ampere's law there will be a difference of
potential between h and c equal to Qmo, whei'e a is the radius of the rotat
ing piece, w its angular velocity, and 9 the vector potential along the
direction of motion of the disc. According to the dielectric theory there
will also be the same difference of potential between h and c if we sup.
pose that there is no discontinuity in tbe motion. We shall suppose that,
instead of the velocity changing abruptly from (oa to zero as we pass
from the rotating conductor to the dielectric, there is a layer of the
dielectric next to the conductor in which the change of velocity is very
rapid, one side of the layer moving' with the velocity wa, the other side
being at rest. Then, using the same notation as before, we have —
'—. '^1/ h'k. __ . — , ^
(It dx\" clt ' ^ dt ' " dt
X=c
dt dy L
dt
dz
dx q(7^/
dt dt
+ H
dt
}
I
Integrating across the thin layer of the dielectric, in which the velocity
is changing rapidly, we see that the difference of jDotential between b
and c equals
where dxjdt, dijjdt, dzjdt are the velocities of a point on the boundary
ON ELECTRICAL THEOEIES. 149
of the moving conductor. This equals Qaw, the same value as that
given by Ampere's theory, so that in this case the two theories lead to
identical results, which are in agreement with the result of Helmholtz's
experiments.
Rontgen has recently published ' a preliminary account of some
experiments which seem to pi'ove directly that the variations in the
dielectric polarisation produce eflPects analogous to those due to a
current.
This completes the account of the experiments which have been made
to test the various theories. As the result of them we may say that they
show that it is necessary to take into account the action of the dielectric,
but they tell us nothing as to whether any special form of the dielectric
theory, such as Maxwell's or Helmholtz's, is true or not.
I have described two experiments which would decide whether
Maxwell's theory that all circuits are closed is true or not. It seems to
me, however, that even if Maxwell's theory be wrong, Helmholtz's is not
the only alternative. I have given a sketch of a theory in which I have
tried to make as few assumptions as possible ; all that I have assumed is
that when a dielectric is acted on by a changing electromotive force,
it behaves like a conductor conveying a current whose intensity is pro
portional to the rate of change of the electromotive force. We know
from experiment that it produces effects of the same character, and I
have assumed as the simplest assumption I could make that for the same
dielectric the equivalent current is proportional to the rate of change of
the electromotive force, so that equivalent current = r/ (rate of change
of electromotive force).
Both Maxwell and Helmholtz assume that rj depends only on the
specific inductive capacity of the dielectric, but I think it is preferable,
until we have more experiments on this point, to look on r) as the measure
of a new property of a dielectric, and not to assume that it is merely a
function of the specific inductive capacity, the only experimental evi
dence for this being the by no means perfect agreement between the refrac
tive index and the reciprocal of the square root of the specific inductive
capacity. To prove Maxwell's theory of closed circuits it would not be
sufiicient to prove that for one medium, say air, r; =::■ K/47i, for it is quite
conceivable that electrical phenomena may be simpler in a dielectric like
air, where the electrical behaviour of the ether seems to be but little
affected by the presence of the dielectric, than in such a one as glass or
other substance possessing a comparatively large specific inductive
capacity, when the effect of the ether is seriously modified by the
presence of the medium.
Since in the theory I have sketched the values of
du d V dvj
dx dy dz
and I (it, — ^(2) + in (u, — v^) + n (wj — iv^)
are not zero, but arbitrary, inasmuch as they involve ?;, in order to find
the value of the force between two circuits where there is any dis
continuity in the currents we shall require to know the value of the
quantity k which occurs in v. Helmholtz's theory.
The most pressing need in the theory of electrodynamics seems to
' Phil. Mag., May. 1885.
150 EEPOET — 1885.
be an experimental investigation of the question of the continuity of tliese
dielectric currents ; we have experimental proof that they exist, but we
do not know whether Maxwell's assumption that they always form closed
circuits with the other cui'rents is true or not. If Maxwell's assumption
should turn out to be true, we should have a complete theory of electrical
action ; if, on the other hand, it should turn out to be wrong, then we
should have to go on to determine the quantity h. This quantity is diffi
cult to determine, as its influence on all closed circuits disappears. It
influences, as v. Helmholtz has shown, the rate of propagation of the
electric potential along conducting wires, and I think we can see that it
would influence the time of oscillation of an irregular distinbntion of elec
tricity over a conducting shell. The easiest way, however, of determin
ing this quantity would seem to be the straightforward one of measuring
electrostatically the value of the electromotive force due to a valuation
in the charge of a condenser ; the expression for the vector potential, as
we saw on p. 140, involves h, so that if we measure the electromotive
force, which is equal to the iate of variation of the vector potential, we
shall determine the value of the vector potential, and consequently of Ic.
Appendix I.
Since the Report was written I have had through the kindness of the
author an opportunity of seeing the advance proofs of a paper by Pro
fessor J. H. Poynting, of Mason's College, Birmingham, ' On the Connexion
between Electric Current and the Electric and Magnetic Induction in
the Surrounding Medium,' which is about to appear in the ' Philosophical
Transactions.'
The views expressed in this paper are rather a new way of looking at
Faraday and Maxwell's theory than a new theory of electrodynamio
action, as however it brings the action of the dielectric into great
prominence it is instructive to consider it.
The paper is largely based on a previous one by the same author on
the ' Transference of Energy in the Electromagnetic Field,'' it is therefore
necessary to give a brief account of this paper.
In it the author shows that the rate of increase of the energy inside
any closed surface equals
^{[{l (R'/5  Q'y) + m (yF  aW) + n («Q'  /3F)}c?S,
where cZS is an element of surface, 1, m, n the direction cosine of the
normal to JS, o, /3, y the components of magnetic induction, and
P', Q', R' given by the following equations : —
p,^_dF_#
dt dx*
^ " dt dif
cm chj.
^ ~ dt dz'
' Phil. Trans., 1884, part ii
ON ELECTBICAL THEORIES. 151
■where r, G, and H are the components of the vector potential and xp ^^^
electrostatic potential ; thus if the medium is at rest P', Q', H' are the
components of the electromotive force at the point.
Professor Poynting interprets this equation to mean that the components
parallel to the axes of x, y, z of the flow of energy across each element of
surface are respectively
2:(R'^QV),
4ir
1 (Q'«  ?'/3),
so that according to this view the energy flows in the direction which is
at right angles both to the magnetic and electromotive forces, and in the
direction in which a righthanded screw would move if turned round
from the positive direction of the electric intensity to the positive
direction of the magnetic intensity ; the quantity of energy crossing in
unit time unit surface at right angles to this direction being
— . Electromotive force at the point X magnetic force
X sine of the angle between these forces.
This interpretation of the expression for the variation in the energy seems
open to question. In the fir.st place it would seem impossible a priori to
determine the way in which the energy flows from one part of the field
to another by merely differentiating a general expression for the energy
ill any region with respect to the time, without having any knowledge of
the mechanism which produces the phenomena which occur in the
electromagnetic field : for although we can by means of Hamilton's or
Lagrange's equations deduce from the expression for the energy the
forces present in any dynamical system, and therefore the way in which
tlie energy will move, yet for this purpose we require the energy to be
expressed in terms of coordinates fixing the system, and it will not do to
take any expression which happens to be equal to it. The problem
of finding the way in which the energy is transmitted in a system whose
mechanism is unknown seems to be an indeterminate one ; thus, for
example, if the energy inside a closed surface remains constant we cannot
unless we know the mechanism of the system tell whether this is because
there is no flow of energy either into or out of the surface, or because as
much flows in as flows out. The reason for this diff'erence between what
we should expect and the result obtained in this paper is not far to seek.
Though tlie increase in the energy inside a closed surface equals
i{KR'/3Q'r) + . • • l^S,
it does not follow that the components of the flow of energy across each
element of surface are (R'/j — Q'y)/^'!', &c., for we can find quantities
u, V, IV which are of the dimensions of rate of change of energy per unit
area, and for which
(lu + mv + niv) dS := 0.
u ■
152 EEPORT — 1885.
The following values of u, v, iv satisfy this condition : —
= 1 / JL. (FG)  ^ (HF) \ ,
t, = i ( JlL^ (GH)  ^ (FG) 1 ,
w = ^( /^' (HF)  f\ (GH) ],
fj.ldx dt ^ ^ dijdt^ ^ r
where /x is the magnetic permeability and F, G, H are the components
of the vector potential, or if i// be the electrostatic potential
«=^{#hJ,^{^^g1,
dy L dz J dz [. dy J
dy L dz J dz {. dy
. = ^(l^FJ^(i^Hl,
dz L dx i dx I dz J
^„=i.(^G"i^{^^p"l,
(/a; L t'y J dy [. dx J
If the values of u, v, w which satisfy these conditions be denoted by
the («!, ^1, w{), {u^, V2, w^ . . . then the flow across any element of
surface might have for its x component —
~(R' ft  Q' y) + Xi «, + Xo u, + \3 % + . . .
where X,, Xj, X^ are arbitrary constants, thus we see that the components
of the flow of energy, instead of being uniquely determined by this pro
cess are really left quite indeterminate by it. Though this is so, it is very
instructive to follow Professor Poynting's description of the way in which
the energy flows in some special cases ; we shall select a very simple one,
the case of a current flowing along a straight wire. Here the lines of
electromotive force are straight lines parallel to the wire, the lines of
magnetic force are circles with their centres on the wire, and their planes
at right angles to it. Then, since according to the view expressed in
the paper, the energy moves at right angles both to the electric and
magnetic forces, it must in this case move radially inwards to the wire
where it is converted into heat. The energy, instead of being supposed
to be transmitted through the wire, is regarded as transmitted by the
dielectric ; and though we may not regard the exact law of flow of
the energy as established, still it is very important that this view
should be brought into prominence. Another important point brought
prominently forward in this paper is the view that magnetic force is
always the sign of transference of energy, according to Professor
Poynting ; indeed, there must be transference of energy from one part of
the field to another to give rise to magnetic force. Thus, according to
his view, no magnetic force would be exerted by the discharge of a leaky
condenser, because in this case he considers the energy to be confined to
the space between the plates of the condenser and to be converted into
heat where it stands. If the plates were connected by a metallic wire,
the energy could flow out and be converted into heat in the wire and
this motion of energy would give rise to magnetic forces, so that magnetic
ON ELECTRICAL THEOEIES, 153
forces wonldbe produced by the discharge of a condenser in this way, but not
by leakage. In this case the theory differs from Maxwell's, as according
to that theory the alteration in the electromotive force w,ould produce
magnetic forces in either case.
In Professor Poynting's second paper, which we have already men
tioned, the fundamental principles of electrodynamics are described as
the results of the motion of the tubes of electromotive and magnetic
force. Maxwell develops electrodynamics from the principles : —
1st. That the total electromotive force round any closed curve is
equal to the rate of decrease of the total magnetic induction through the
curve.
2nd. The line integral of the magnetic force round any closed curve
is equal to 4:ir times the current through the curve.
Professor Poynting restates these principles in the following way : —
1. ' Whenever electromotive force is produced by change in the mag
netic field, or by motion of matter through the field, the E.M.P. per
unit length is equal to the number of tubes of magnetic induction
cutting or cut by the unit length per second, the E.M.P tending to
produce induction in the direction in which a righthanded screw would
move if turned round from the direction of motion relatively to the tubes
towards the direction of the magnetic induction.'
The second principle he states in the following way : —
' Whenever magnetomotive force is produced by change in the electric
field, or by motion of matter through the field, the magnetomotive force
per unit length is equal to 47r times the number of tubes of electric
induction cutting or cut by unit length per second, the magnetomotive
force tending to produce induction in the direction in which a right
handed screw would move if turned round from the direction of the
electric induction towards the direction of motion of the unit length
relatively to the tubes of induction.'
By magnetomotive force is meant the line integral of the magneto
motive force round a tube of induction. This statement includes the
more special one that the line integral of the magnetic force round any
closed curve is equal to 4m times the number of tubes passing in or out
through the curve per second.
The development of these principles leads to equations which are
practically the same as those obtained by Maxwell, the chief difference
being that the quantity corresponding to Maxwell's J is no longer
arbitrary or rather redundant.
Professor Poynting also introduces into his equations the time
integrals of the components of the magnetic force as fundamental quan
tities, and regards the components of the magnetic as the differential
coefficients of these quantities with regard to the time. This method of
representing magnetic force was also used by Professor Fitzgerald in his
paper on the Electromagnetic Tlieory of the Reflection and Refiaction
of Light.' It has the advantage of calling attention to the dynamic
character of magnetic phenomena. In Professor Poynting's paper some
of the applications of his method of regarding electrical phenomena are
worked out with great detail for some of the simpler cases.
■ PMl. Trans., 1880, part ii.
1<'54 EEPOET — 1885.
Appendix II.
ON THE STRESS IN THE DIELECTRIC.
In the preceding Report we have had so frequently to refer to the
action of the dielectric that it may be convenient to give a very brief ac
count of the work which has been done on the stresses which are sujDposed
to exist in it. We shall confine ourselves to the work which has been
done on the stresses in the electrostatic field; those existing in the electro
magnetic field are of a similar nature, so that any remark applying to
one will also apply to the other. The idea of explaining the forces
in the electrostatic field by means of stresses in the dielectric seems to be
due to Faraday, who describes ' the stress in the medium by sayiug that
the lines of force tend to contract and also to repel one another. The
magnitude and distribution of this stress was investigated by Maxwell ; ^
he found that in a medium whose specific inductive capacity was K, and
at a point where the electromotive force is E, a tension equal to KR^/Btt
per unit area along the lines of force combined with a pressure of the
same amount at right angles to these, would produce the effects observed
in the electrostatic field, that is, at a point in a dielectric, the resultant of
these stresses would be a force whose components, parallel to the axes of
X, y, z, are eX, eY, eZ respectively, e being the charge of electricity at the
point, and X, Y, Z the components of the electromotive force. It may be
observed that this system of stress could not be produced by the strain
in an elastic solid at rest : this points to the kinetic origin of "electrostatic
phenomena.
These stresses are in equilibrium at a point in a dielectric where there
is no free electricity. At the junction of two media, whose specific inductive
capacities are K, and Kg, and in which the electromotive forces are
Ri and Rj, and whose interface is perpendicular to the lines of forces,
the stresses are not in equilibrium, but there is an unbalanced stress
(Kj Ri" — Ko Rj) /Stt which will tend to make the boundary move
towards the medium whose specific inductive capacity is Kj ; if these
dielecti'ies are liquids, their interface may become curved so that the forces
due to surface tension balance this stress.
Quincke,^ who has experimentally investigated the effects of electrifi
cation on various dielectrics, such, for example, as the efiects on the glass
of a Leyden jar, has found that the efi'ects on difi^erent bodies aie very
different ; he finds, for example, that though the effect of the electrification
on the dielectric of the Leyden jar is generally to produce an expansion,
yet^ in some substances, such as the fatty oils, contraction takes place.*
This diversity in the effects of electrification on different dielectincs shows
that the distribution of stress cannot be so simple as was supposed by
Maxwell. It also shows that there must be forces in the electric field
which are not recognised either by Maxwell's theory or the theory of
action at a distance. More general theories have been given in order to
meet this difficnlty.
' ExjjeTiiHeiital Eesearchcs, § 1 297.
^ Wectrioity and Magnetism, 2ncl edition, p. 149.
3 Wiecl. Ann., x. pp. l(jl, 374, 513; IMd., ix. p. 105; Pidl. Mag., yo\.:^. n. ZO
(1880). I ' J ' I
* The fatty oils are also an exception to the rule that the index of refraction
equals the square root of the specific inductive capacity.
ON ELECTEICAL THKOEIES. 155
T. Helmholtz ' lias supposed tliat a change in the density of a dielec
tric might alter its specific inductive capacity, and he has investigated
the consequences of this supposition. Korteweg and Lorberg ^ have
investigated the more general case, when the specific inductive capacity
of a strained dielectric is supposed to be a function of the strains.
Korteweg supposes that if the body suffers dilatation e along the lines of
force, and dilatations / and cj at right angles to them, then the specific
inductive capacity = K— ae— /3 {f+g) Helmholtz assumed that
a = /3. The presence of strain in a dielectric must influence the specific
indiTctive capacity, for Quincke has shown that the various coefficients of
elasticity are altered under the influence of electricity. Lorberg, I.e., has
found the distribution of stress in the medium when the specific inductive
capacity alters in this way. He finds that there is a tension along the
line of force equal to
and a pressure at right angles to them equal to
KStt 2 J
The force in the medium parallel to the axis of x
where
*±7r tCit/ tltl/ tviO tltt' tvU tlAf till
+ _^ (a/3) ^^
dz dx dz
Where is the potential, and p the volume density of the free electricity.
The part A of this force exists even when there is no free electricity at
the place under consideration ; if the dielectric were a fluid, these terms
would indicate forces tending to move the fluid when placed in a variable
electx'ic field ; this motion, however, seems not to have been observed.
The supposition made by Korteweg and Lorberg is not the most general
one that could be made ; we might assume that the specific inductive
capacity of the strained body became difl'erent in different directions, So
that the body would behave like a crystal. Dr. Kerr's experiments on
the double refraction in liquids placed between the poles of a powerful
electrical machine seem to point to this conclusion.
Kirchhoff ^ has made similar assumptions to those of Korteweg and
Lorberg on the effect of strain on the specific inductive capacity, and has
arrived at similar equations ; in the second paper he applies these equations
to some cases which Quincke investigated experimentally.
' V. Helmholtz, Wied. Ann., xiii. p. 385; WissenscJiaftl. Abh. vol. i. p. 298.
^ Korteweg, Wied. Ann., ix. p. 48 ; Lorberg, Wied. Ann., xxi. p. 300.
' Wied. Ann., xxiv. p. 52, 1885 ; Ibid., xxv. p. 601, 1885.
156 EEPOET— 1885.
Second Report of the Committee, consisting of Professor Schuster
(Secretary), Professor Balfour Stewart, Professor Stokes, Mr.
Gr. Johnstone Stoney, Professor Sir H. E. Eoscoe, Captain
Abney, mid Mr. Gr. J. Symons, appointed for the purpjose of
considering the best methods of recording the direct intensity of
Solar Radiation.
The Committee, working on tlie lines of their last report, have given their
attention to the best form of a selfrecording actinometer, and have come
to the following conclusions : —
1. It seems desirable to construct an instrument which would be a
modification of Professor Stewart's actinometer adapted for selfregistra
tion — the quantity to be observed being, not the rise of temperature of
the inclosed thermometer after exposure for a given time, but the excess
of its temperature when continuously exposed over the temperature of the
envelope.
2. As the grant to the Committee will not admit of the purchase of
a heliostat, it will no doubt be possible to procure the loan of such an
instrument, and, by making by its means sufficiently numerous com
parisons of the instrument proposed by the Committee with an ordinary
actinometer, to find whether the arrangement suggested by the Committee
is likely to succeed in practice. The Committee would therefore confine
their action for the present to the carrying out of such a series of
comparisons.
3. The size of the instrument might be the same as that of Professor
Stewart's actinometer.
4. The instrument should have a thick metallic enclosure, as in the
actinometer above mentioned, and in this enclosure there should be
inserted a thermometer to record its temperature. Great pains should
therefore be taken to construct this enclosure so that its temperature shall
be the same throughout.
5. The interior thermometer should be so constructed as to be readily
susceptible of solar influences. It is proposed to make it of dark glass,
of such kind as to be a good absorber, and to give it a flattened surface
in the direction perpendicular to the light from the hole.
6. It seems desirable to concentrate the sun's light by means of a
lens upon the interior thermometer, as in the ordinary instrument. For
if there were no lens the hole would require to be large, and it would be
more difficult to prevent the heat from the sky around the sun from
interfering with the determination. Again, with a lens there would be
great facility in adjusting the amount of heat to be received by employing
a set of diaphragms. There are thus considerable advantages in a lens,
and there does not appear to be any objection to its use.
The Committee have not drawn their grant (201.). They suggest
that they be reappointed, and that the unexpended sum of 20?. be again
placed at their disposal.
ON OPTICAL THEORIES. 157
Report on Optical Theories.
By E. T. GLAZEBROOK, M.A., F.R.S.
Dk. Lloyd's wellknown Report on Physical Optics was presented to the
Association at its meeting in Dublin in 1834 — fiftyone years ago. Since
that time the question of double refraction has been treated of very fully
by Professor Stokes in the Report for 1862, but unfortunately he con
fined himself to that one branch of the subject. The years immediately
succeeding that in which Dr. Lloyd's report was read were mai'ked by
work of great importance, which has formed the basis for much that has
since been done, and it is necessary, before writing of recent progress in
the subject, to consider somewhat carefully the researches o£ Green,
MacCullagh, Cauchy, and F. Neumann.
This 1 propose to do, in as brief a manner as possible, for that part of
the subject which is not included in Professor Stokes's report. I then
propose to go on to the consideration of more modern work, treating sepa
rately (1) of the simple elastic solid theory, (2) of theories based on
the mutual reactions of matter and ether, (3) of the electromagnetic
theory.
PaKT I. — IXTRODUCTION.
THE WORK OF MACCULLAGH, KEUMANy, GREEN, AND CAUCHY.
Chapter I. — MacCullagh.
§ 1. Fresnel ' himself had developed a theory of reflexion and re
fraction, and had arrived at formulas giving the intensities of the reflected
and refracted waves in terms of the incident.
In obtaining these he relied on the two following principles : —
The resolved parts of the displacements parallel to the face of inci
dence are the same in the two media.
The total energy in the reflected and refracted waves is equal to that
in the incident wave.
He further supposed that the rigidity of the ether is the same in all
transparent media, and hence that reflexion and refraction are produced
by a change of density ; from this it follows that the refractive index of
a medium is proportional to the square of the density of the ether in the
medium. The direction of vibration is considered to be perpendicular to
the plane of polarisation. According to this theory there is a discon
tinuity in the component of the vibration at right angles ^ to the surface.
§ 2. An elegant geometrical expression of the laws to which these
principles lead was given by MacCullagh. He defines as the trans
versal of a ray the line of intersection of the wave front and the
plane of polarisation ; the length of this line being proportional to the
' Fresnel, Ann. dc Chlm. et do Physique, t. xlvi. p. 225 ; (Eiivres completes,
t. i. p. 767.
^ For a further consideration of this point see p. 186.
158 EEPOBT — 1885.
amplitude of the vibration multiplied by tbe density of tlie medium.
Then Fresnel's results may be expressed by the statement that the trans
versal of the incident ray is the resultant, in the mechanical sense of the
word, of those of the reflected and refracted rays.
This first suggestion of MacCullagh's was modified by reading some
of Cauchy's work on double refraction, from which it appeared possible
that the vibrations of polarised light might lie in the plane of polarisa
tion instead of at right angles to it. Adopting, then, this hypothesis,
a transversal represents in addition the direction of vibration ; and if the
further supposition is made that the ether is of the same density in all
media, so that reflexion and refraction arise from variations in its
rigidity and not in its density, expressions very nearly identical with
Fresnel's can be found for the intensities of the reflected and refracted
rays, while at the same time the principle of the continuity of the
displacement normal to the surface is satisfied.
§ 3. These three principles —
(1) The ether is of the same density in all media,
(2) The displacement is the same on both sides of the surface of
separation of the two media,
(3) The energy of the incident wave is equal to that of the reflected
and refracted waves
— were applied by MacCullagh to the problem of reflexion and refrac
tion at the surface of a crystal, and the results of a first investigation
were communicated to the meeting of the Association in 1834.
The theory as there given was somewhat modified in consequence of a,
paper by Seebeck in Poggendorif 's ' Annaleu,' and took its final form in
a memoir read before the Irish Academy ' in January 1837. MacCuUaoh
in this paper states his fundamental principles, not as based on mechanics,
but merely as those which had led him to a solution, the results of
which agree closely with the experiments of Seebeck and Brewster.
The analysis of the problem is greatly simplified by the introduction
of the idea of ' uniradial directions.'
In a crystal, for any given direction of incidence, there are two posi
tions for the incident transversals, which give rise each to only one
refracted ray — there are corresponding positions for the reflected trans
versals. These directions of the incident transversals are the uniradial
directions.
For a uniradial direction the incident, reflected, and refracted trans
versals lie in one plane, and the refracted transversal is the resultant of
the other two.
The transversal is normal to tlie plane containing the ray and the
wave normal. The polar plane is defined as a jDlane through the trans
versal and parallel to the line joining the extremity of the ray to the
point in which the wave normal meets the surface of wave slowness, here
designated the ' index surface.'
It is hence proved that for a uniradial direction the incident and
reflected transversals lie in the polar plane of the refracted ray, and then
the principles of equivalence of vibrations and of vis viva lead to
equations to determine the relation between the azimuths of the trans
versals referred to the plane of incidence.
' lyiacCullagh, ' On the Laws of Crystalline Reflexion and Eefraction,' Januarv,
1837, Trans, of Royal Irish Academy, vol. xviii.
ON OPTICAL THEORIES. 159
These give —
tan 6 = cos (<p  f') tau 6' + si" Y tan x
cos d' sin ((f) + f')
(1)
tan 0, =  cos (^ t d,') tan 8' + sm »ja^nj^_
cos d' sin (^ — 0')
with exactly similar formate for the other uniradial direction ; ft, 0;, and
ti' are the azimuths of the transversals in the incident, reflected,'and re
fracted waves measured from the plane of incidence, and % tlie ano'Ie
between the ray and the wave normal. In the general case the incident
vibration is resolved into two in the uniradial directions, and each
considered separately. When the two values of «,, found from these, are
equal, the partial reflected transversals coincide ; the value of ^i at which
this takes place is the deviation, and the angle of incidence the polarising
angle.
The theory is applied to Iceland spar, and agrees with experiments of
Brewster and Seebeck.
§ 4. The same problem is considered by Neumann ' in a long paper
read in 1835 before the Berlin Academy, and in a second memoir pub
lished separately in Berlin 2 in 1837, and the same results deduced from
similar hypotheses.
§ 6. In 1839 MacCullagh ^ attempted to found his theory on a dyna
mical basis by finding an expression for the potential energy of the ether
when strained by the passage of the waves of light, and applyino to the
expressions thus obtained Laplace's principle of virtual velocities.'^
This leads to a volume integral which holds throughout the space
occupied by the medium, and a surface integral to be taken over the
boundary.
The surface integral taken in connection with the principle of the
continuity of the displacement gives the conditions at the surface and
these are shown to be identical with the conditions found in the previous
paper. ^
Professor Stokes, in the Report on Double Refraction, has pointed out
the error in the fundamental expression assumed by MacCullaoh for the
energy, and this error of course affects the theory of reflexion. ^
Chapter II. — Geeen.
§ 1. The correct expression for the energy, and the correct laws of re
flexion and refraction on a strict elastic solid theory, had at the date of
MacCullagh 's paper been given by George Green * in a memoir read before
the Cambridge Philosophical Society in December 1837.
The potential energy of the medium is shown to be a function U)
ot tJie three principal elongations s„ s^, s^, and the three principal
shearing strains a, /3, y. ft'
,'^.^y''\"^^'^^^Tetische Untersuchuug der Gesetze nach welchen das Licht an
der Granze zweier vollkominenen durchsichtigen Medien reflectirt und gebrochen wird°
dieInw'u•T;,^'^''■•.'^?^^^^^^^^' "^"^ Krystallfliichen bei der Reflexion und ttber
^i!.r^l l"^* "^""^ gewohnlichen und ungewohnlichen Strahls.' See also ' Vorlesuo^en
fiber tWtische Optik,' von Dr. F. Neiimann, edited by Dr. E. Dorn. Leipzi' sfs
«r,dP t'^r"'"^.^'^'^ Essay towards a Dynamical Theory of CrystaS Reflex 'on
and Refraction,' Tram, of Royal Irish Academy, vol. xxi. ^enexion
Geo. Green, ' On the Laws of Reflexion and Refraction of Light at the fommnn
160 KEPORT — 1885.
This function is then expanded in the form
? = V>0 + </>i + '/>2 +• • • •
00, &c., being homogeneous functions of the orders 0, 1, 2 of the small
quantities Sj, s^, &c.
The equations of motion depend on '60, and so, (po being constant, it
does not appear. If the medium in its equilibrium position is unstrained
01 vanishes also, and in general 02 contains twentyone arbitrary coeffi
cients. 03 may be neglected compared with 02 If the medium be not
initially free from strain, 0, will introduce six more coefficients, so that
finally we find the most general form of for our purposes involves
twentyseven coefficients. •
Green then supjDOses the medium to be symmetrical with regard to
three rectangular planes, and obtains finally as the form for f, taking the
case in which the medium is initially strained, the value —
_20=2A*'f2B*^H2C 5'
^ civ dy az
, ^T^ dv dvj , or\ <^" (^^y 1 OT? '^"^ ^'"
dy dz dx dz dx dy
+
+ G
+ L
ydz dy J \dz dx) \dy dxj ^ ^
If the medium be initially unstrained A=B=C=0, while, further, if
it be completely isotropic,
G = H = I = 2N fR"!
L = M = N j» . . . . (2)
P = Q = R. J
And introducing two new constants, A and B,
n^ . fdn , dv . dw\^
— 202 = A  + •— + y
^^ \dx dy dz )
. (dv dw , dw du du dv\ \ ^o\
\dy dz dz dx dx dy) J
■ For the difference between this and Cauchy's theory see Prof. Stokes's report.
ON OPTICAL THEORIES.
161
According to Green's theory of double refraction, founded simply on
the supposition that the displacements are in the wave front in a crystal,
G = H := I = /i, say
Q=/i2M f
The equations of motion are given by
j^^Mjdz[p(piu
^d<p\ =0
(4)
(5)
In treating of the problem of reflexion this integral is applied to the
whole of the two media, and is transformed by partial integration into a
volume integral, which may be written
and a surface integral, which we may write
\dy dz (X cu — Xj cmj)
+ dzdx(Jlv — Yylv{)
+ dx dy {7i Iw — Zj Iw^.
These two integrals must vanish separately. Green's work as to the
former, on which the propagation of light depends, has been considered
by Professor Stokes. It leads to the three equations —
^^" /A o\ ^ fd^*' , dv , div\ , Tj „ 9
' df^
— (K — TV\ / 1 4 ^ 4 R V7 2
dy \dx dy dzj
d^io
d /du dv div^
dz \dx dy dz ,
p— =(AB)^J^^ + ^ + ^^) + Bv^^«
(6)
which form the basis of the whole theory of isotropic elastic solids,
§ 2. The latter integral equated to zero gives us the surface condi
tions ; for over the surface, according to Green, who treats the ether in
the two media as two separate elastic solids always in contact with each
other, we must have
• . . (7)
• • . (8)
and hence
«=Mi, t;=fi, w=w^,
X=Xi, Y=Ti, Z=Z,,
These six equations determine the motion completely.
Using Green's notation, and considering only the case of two homo
geneous media, let us take the plane x=0 as the separating surface.
Then the surface conditions become
1885.
i(=M^, V^Vi, W = lVi,
M
162
REPORT — 1885.
\dx dy dz J \dy dz J
. Aiwi dvj . r?WiN _ 22 A7f'i , dw^ \
\dx dij dz J ' V% d7. J
rdu dv\ _ g I'dxi _^ dvi\
\dy dxj ' V dy dx J
fdu div\ _ o (dMi ,dw^\
\di "^Ite; '\dz^ dx J
B
B
. (9)
when a;=0.
The problem now resolves itself into two cases. Let ns take the plane
of incidence as the plane xy, and suppose that the vibrations in the
incident wave are perpendicular to this, then —
Case I. — Light polarised in the plane of incidence,
and the conditions are
T) dw r, dw]
dx
dx
}
(10)
Now, we have seen that Fresnel originally assumed that the rigidity of
the ether is the same in all media, and the density different. Green,
adopting this view, puts B=Bi, A=Ai,* and the above formula lead him
to results agreeing with those given by Fresnel's simple theory for this
case, while, by making the angle of iefraction imaginary, it is shown that
the wave, when totally reflected, undergoes just the change of phase given
by Fresnel.
Case II. — Light polarised at right angles to the plane of incidence, the
vibrations being therefore in that plane.
Then i(; = t(;i=0, and the surface conditions are
U = U,, V = V,
Z«,
" \ dx dy) dy \ dx dy ) dy
= R, f'^'^i^.'^ll)
ry/du dv
\dy dx,
. (11)
J ' V dy dx
We have here four equations to determine two unknowns, viz. the inten
sities of the reflected and refracted rays, and it is clear, therefore, that
two more quantities must come under consideration.
Now, in the general case it follows from the equations of motion given
above that two waves can traverse the medium. In the one of these the vibra
tions are transverse, and travel with the velocity \/B/p. This constitutes the
liohtwave. In the other the vibrations are longitudinal, and travel with the
velocity^ A /p. In the case before us, then, reflexion gives rise to both
these, and we have two reflected and two refracted waves. But experi
* The physical meaning of these constants and the relations implied by these
conditions will be considered later, see p. 167.
ON OPTICAL THEORIES. 163
ment tells us, id a bigli degree of approximation, that the whole of the
energy of the incident light appears in the reflected and refracted light.
"We are therefore forced to suppose not merely that the longitudinal wave
does not affect our eyes as light, but also that it does not absorb any
material part of the incident energy. This conclusion is confirmed when
we recollect that on arriving at a second refracting surface this longi
tudinal wave would, if it existed, set up transverse vibrations which
would be visible, so that on passing through a prism, for example, there
would always be two emergent rays.
Now, Green shows that very little energy will be absorbed by the
longitudinal vibrations, provided that the ratio A/B be very small or
very great ; and, further, that the condition of stability of the medium
requires that A/B should be greater than 4/3. He therefore concludes
that A/B is very great — practically infinite, or that the wave of longi
tudinal vibrations travels with a velocity enormously greater than that of
light.
The equations are then solved, assuming that B = Bj and A = Ai,* by
the substitutions —
eld) , d4'\
dz dij
d^_d\li
dy dx
(12)
The symbol represents the longitudinal or, as Sir Wm. Thomson
has called it, the pressural wave, and \p the transverse or light wave.
It is shown that by the reflexion a difference of phase is produced
between the reflected and incident and the refracted and incident waves,
and expressions are found for the intensities of the reflected and refracted
waves in terms of that of the incident. According to these expressions,
the mtensity of the reflected wave never vanishes, but reaches a minimum
when f + <p'z= 90°. The minimum value of the ratio of the two intensi
ties will be for air and water about 1/151, while for a diamond or other
substance of great refractive index it would be much greater still.
§ 3. This result, then, of the theory is in direct antagonism to the fact
that light is very nearly completely polarised by reflexion from most
transparent surfaces at the polarising angle, while the values found for
the change of phase do not agree with the experiments of Jamin,'
^mcke, and others, and the theory as left by Green is certainly incorrect.
We shall, however, return to this point later.^
Green does not apply his equations to the problem of crystalline
reflexion, and, indeed, his theories of reflexion and of double refraction are
entirely inconsistent, for the former supposes the ether to have the same
rigidity in all bodies, while the latter attempts to explain double refrac
tion by making the rigidity of a crystal a function of the direction of the
strain,
* This last equation, as we shall see later, is not necessary.
Jamin, Ann. de Chimie (3), t. xxix. p. 263 ; Quincke, ' Experimentelle optische
^ntersuchungen,' Pogg. Ann. See also Haughton, Phil. Mag. (i), vol. vi. p. 81.
* See p. 192. ^ ^ ■/' t;
M 2
164 EEPOKT — 1885.
Chapter III. — Cauchy.
§ 1. Cauchy 's optical researches were being published about this
same period, and a very full and interesting account of them, and of the
work of other French authors, is given by M. de St. Venant in a paper to
which I am greatly indebted for much valuable information.'
Cauchy 's work on elastic solids began in 1822, and in 1829 he pre
sented to the Academy his first memoir on isotropic media. His more
generally known memoir followed in 1830,^ containing his work on
double refraction and the propagation of light in a crystal. An account
of this is given in Professor Stokes's report in 1862. His first work on
dispersion, which he explained (following a suggestion of Coriolis) by the
addition of terms involving differential coefficients above the second, was
published in 1830.^ The great memoir, ' Sur la dispersion de la
lumicre,' in which he developed this principle, appeared between 1830 and
1836 ; ■* and in this same memoir he first considered the problem of reflexion
and refraction, which led him to the idea of elliptic polarisation and
a more general expression for the possible displacements of a molecule *
in a plane wave.
§ 2. Further considerations on the subject of reflexion and refraction
led him to conclude that, in order to obtain Fresnel's expressions for the
intensities of the reflected and refracted rays in terms of that of the
incident, it was necessary that not only the displacements, but their
differential coefficients with respect to the normal to the surface of
separation, should be continuous across that surface. This continuity
had to be rendered compatible with the rest of his theory, in which the
ether is considered as differing both in density and elasticity in different
media.'* It is, however, quite inconsistent with the true surface con
ditions established by Green, Neumann, and MacCullagh on their various
hypotheses — the conditions, namely, that the displacements and the stresses
over the surface should be the same in the two media; and Cauchy, in con
sequence, was led to conclude that the method of Lagrange, by which the
above conditions were first established, is inapplicable to questions of this
kind.^ But, as St. Venant points out, these suiface conditions do not in
the least depend on Lagrange's method of virtual velocities, but on the
fundamental elementary principles of mechanics, and can never be recon
ciled with Caucliy's theory of continuity so long as it is supposed that
the rigidity of the ether varies from one body to another.
§ 3. In 1839 * Cauchy reestablished his equations of motion for an
isotropic medium, basing them on analytical considerations of symmetry.
For a perfectly isotropic body he arrived at the equations —
p^=(AB)f + Bv2« . . . (13>
dt'^ dx
, „ dti , dv dw
Ac, where ^ = Tx'^^j^^'
' De St. Venant, 'Sur les diverses mani^res de presenter la thSorie des ondes
lumineuses,' Ann. de Chimie (S. iv.), t. xxv. p. 335.
" Cauchy, Exercices de Mathcmatiqncs, t. v. pp. 1972.
' Cauchy, Bidletin de M. dc Fcrusmc, t. xv. p. 9.
* Noumaux Exercices de Mathimatiques. * C. It. t. 'vii. p. 867.
» a R. t. viii. p. 37i ; t. x. p. 266.
' C. R. t. xxvii. p. 100 ; t. xvi. p. 1.54 ; t. xxviii. pp. 27, 60.
• C. R. t. viii. p. 985; Exercices d'Anahjsc, t. i. p. 101.
ON OPTICAL THEORIES. 165
already given by Green. ^ And in cases in whicli the axes can only be
turned together aboat the origin, a third coefl&cient comes in, in the form
of terms, such as
p fdw dv
\dy
_dv\
dzj'
In 1849 ^ Cauchy propounded the idea that the ether atoms in a body
such as a crystal are disposed, as it were, in shells round the matter atoms
in such a manner as to have different elastic properties at different points
of the same shell ; the shells, however, are regulai'ly placed, and the
properties of the ether repeat themselves at similar points in the different
shells. It results from this that the constants in the equations of motion
will be periodic functions of the equilibrium positions of the molecules,
and for optical effects we hare to do with the average displacement over
a small volume of the medium.^
The general equations established by Cauchy lead to a normal wave
travelling with a velocity equal to \/A/p. According to his earlier theory,
resting on the law of action between the molecules of ether, A and B are
not independent, and it is possible by suitably choosing the law of force
to make A vanish or even be negative. The theory * of reflexion and
refraction led him to conclude that A was a small negative quantity, so
that the normal disturbance ceases to be propagated as such.
§ 4. Canchy's work was continued by Briot,' starting from the
equations of motion deduced from the mutual action between two par
ticles of ether, and the supposition suggested by Cauchy that the ether
within a crystal is in a state of unequal strain. In treating of dispersion
Briot points out that it cannot be explained in the manner originally
suggested by Cauchy, for there is no reason why the terms in his differ
ential equations from which it arises should be insensible in a vacuum if they
are sensible in ordinary transparent media. He therefore makes it depend
on terms arising from a periodic distribution of the ether within material
bodies, and shows that to obtain Cauchy's dispersion formula the law of
action between the molecules must be as the inverse sixth power of the
distance. In his memoir on reflexion and refraction, however, he adopts
Cauchy's views as to the disappearance of the normal wave, and this is
quite inconsistent with the above law, while the ether and matter mole
cules must attract each other with a force varying as the inverse square
of the distance.
§ 5. The problem of reflexion and refraction for both isotropic and
crystalline bodies is treated of in a memoir published in 186667,^ start
ing from Cauchy's principle of continuity, to which he gives an extended
meaning in the second memoir. He at first supposes the vibrations in
the crystal to be rigorously in the plane of the wave, and, adopting
MacCuUagh's methods of the uniradial direction, arrives at his equations.
The work is then extended to the general case in which the vibrations
o^
' See p. 161.
' a R. t. xxix. pp. 611, 644, 728, 762 ; t. xxx. p. 27.
' For the further development of this by M. SaiTau, see p. 174.
* C. R. t. ix. pp. 677, 727, 76.5. On this point cf. Green's theory. See also
Stokes's, Brit. Assoc. Report, 1862, and pp. 170195.
* Briot, Essais siir la theorie mathematiqiie de la lumiere. Paris, 1861.
' Liouville's Jouriial, t. xi. p. 305 ; t. xii. p. 185.
166 EEPOBT— 1885.
are quasitransversa], and it is shown how the simpler forms of the
equations are modified by this.
Thus, for the uniradial directions in the case in which the longitudinal
disturbance is supposed to be strictly normal to the wave, if ^ is the
angle between the ray and the wave normal, 6, 6', and 0, the azimuths
of the planes of polarisation, measured from the plane of incidence, of the
incident reflected and refracted waves, (p and f' the angles of incidence
and refraction, and m a quantity depending on the angle between the
plane of the wave and the direction of vibration, then —
tan 6 = tan 0' cos (0 — (//) + . — ~ —^
cos sin (</< t ?' )
, /■; /. . /\ '"' sin^ (/>' tan v
tan 0, = tan 0' cos (^ + 0') — ^ ^
(14)
cos W' sin ((^ — 9')
These formulte agree with those of MacCullagh if we put m = 1.
Chapter IV. — Elliptic Polarisation. Compaeison of Results,
§ 1. The peculiar phenomena presented by quartz had been explained
by Airy in 1831 ^ on the assumption that the two waves were elliptically
polarised. In 183G ^ MacCullagh made a further advance, and showed
how the addition of certain terms to the diflFerential equations of motion
would lead to the elliptic polarisation required by Airy's theory. The
equations assumed by MacCullagh, for the existence of which he does
not attempt to assign a mechanical reason, were —
Ti^ ~ 7f? Iff ,
Where A ^ a\ B = a"  {a"  1"") sin^ 9,
(15)
a and h being constants, and the angle between the optic axis and
the wave normal — the axis of z. The two waves resulting from these
equations are shown to be elliptically polarised, while their velocity is
given by the equation
KA)(i.^B) = ^ . . . (16)
X being the wave length. The rotation of the plane of polarisation
produced by the passage of a plane polarised ray through a plate of
crystal cut at right angles to the axis, and of unit thickness, is 'lJz'^Cja^X^.
MacCullagh shows that the results of this hypothesis as to the form
of the equations agree fairly with Airy's experiments, and that the
agreement would be made somewhat more close by the hypothesis that C
varies slightly with 0.
' Airy, ' On the Nature of tlie Two Eays produced by the Double Eefraction of
Quartz,' Camh. Phil. Soc. Trans, vol. iv. pp. 70, 198.
^ MacCullagh, ' On the Laws of the Double Refraction of Quartz,' Irish Trans,
vol. xvii. p. IGl.
ON OPTICAL THEOEIES. 167
§ 2. Terms of a similar kind were first applied by Airy ' to explain
the magnetic rotation of the plane of polarisation discovered by Faraday.
Airy starts by calling attention to the fundamental difference between
the rotation produced by quartz and that due to magnetic action. In
quartz, sugar, etc., by reflecting the ray back along its original path the
rotation is reversed, so that the ray emerges with its plane of polarisation
unaltered, while in bodies under magnetic action the rotation is doubled
by the same process. It is as if the former effect were due to a heliacal
arrangement of the molecules, the latter to a continuous rotation of them
round the lines of force. Airy shows that the effects produced can be
accounted for by the introduction into the equation for u of terms
involving odd differential coefficients of v with respect to the time, and
he works out the case in which the equations are
W ~~ dz^ dt
cPv . d^v _ f>,dzi
clr'~ d? dt .
The two possible velocities for a wave of period r are given by
Vi^ =■ — ■ , f J = .
(17)
It is pointed out also that terms such as — r — or would also
dz^dt dfi
lead to the effect observed ; though they would differ in the law, express
ing the relation between the velocity and the wave length. Airy
remarks that ' the equations are given, not as offering a mechanical
explanation of the phenomena, but as showing that they may be ex
plained by equations, which equations appear such as might be intro
duced by some plausible mechanical assumption.'
§ 3. The attempt to estimate the relative value of the theories of
reflexion and refraction just developed is rendered easier if we consider
the physical meaning of the two constants involved. The importance of
this has been continually insisted upon by Sir Wm. Thomson ^ in his
numerous writings on the subject of elasticity, which have done so much
to clear away difficulties and obscurities ; and though these writings
belong to the later period of our subject, we shall consider here some of
the results they lead to.
To Green, Cauchy, and MacCullagh, A and B are constants, appearing
m the most general form of the equations, and on which the rate of propa
gation of waves depends ; their connection with the other physical pro
perties of the solids is not considered. Now an isotropic 'elastic solid is
one which possesses the power of opposing resistance (1) to change of
shape, (2) to change of volume, and has in consequence only two prin
cipal moduluses of elasticity.
' ^iiTi 'On the Equations applying to Light under the Action of Magnetism,'
PMl. Mag. (.S), vol. xxviii. p. 469.
" See especially, Thomson, ' Elements of a Mathematical Theory of Elasticity,'
Phil. Tram. 1856, p. 481 ; Thomson and Tait, A Treatise on Natural Philosophy,
vol. i. ; Thomson, article ' Elasticity,' Encyclojitedia Britannica, ninth edition, 1880.
168 KBPOET — 1885.
On fhe value of the one, the rigidity, n, in the notation of Thomson
and Tait, depends the resistance which the body can oppose to a stress
tending to produce distortion or change of shape without change of
volume, and it is measured by the ratio of the shearing stress — or stress
tending to produce distortion — to the strain or alteration of shape pro
duced. It can be shown that this is equal to the constant, B, of Green's
theory. And the velocity of a wave of transverse displacement, since it
does not produce changes in the volume of the body through which it
passes, depends only on the ratio of the rigidity to the density.
On the value of the other principal modulus depends the resistance
which the body can ofier to compression or change of volume when sub
jected to a uniform hydrostatic pressure at all points of its surface. The
compression produced is measured by the ratio of the change in volume
to the original volume, and the modulus of compression, k, is the ratio of
the stress to the compression it produces.
It has been shown by Thomson that the relation between A and the
principal moduluses is given by the equation A =: 7^ + f n, so that 1c, the
modulus of compression, is equal to A — fB.
The expression for the stresses arising from simple elongations e,f, g
in the directions of the axes, and from simple shears a, /3, y round the
axes, are found ; they are
^, = (h + in)e+ (lcin)(f+g)
= {k + n)(e +/+ g)2n(f + g)
. fdu ,dv dw\ _ QD fdv clio\
\dx dy dzj \dy dzj^
etc., using Green's notation, and
= na =Bf
dz dy) '
etc., and from these Green's expression for the energy can be obtained.
We may note that the velocity of propagation of the longitudinal waves
^/ A/p depends on both the modulus of compression and the rigidity.
According to the mathematical theories of Navier, Poisson, Cauchy,
and De St. Venant, there is a definite relation between n and h for all
bodies given by the equation n =■ ^h or B ^ ^A. Stokes ' was the first
to point out that this could not be true universally, and this conclusion
has been confirmed by the experiments of Wertheim and Kirchhoff for
various metals.
Thus, on the assumption that the properties of the ether are those of
an elastic solid, Cauchy's theory in its original form, independently of the
consideration of his surface conditions, must be rejected. In his later
theory, as we have said, he does admit the second constant A.^ But, we
have seen that the existence of the two constants A and B implies that
there will be two waves in the medium, while the absence of the wave of
normal vibrations in light, combined with the conditions of stability,
requires that A should be great compared with B, and this again requires
that h, the modulus of compression, should be great compared with n, the
* Stokes, ' On the Friction of Fluids in Motion and the Equilibrium and Motion
of Elastic Solids,' Trans. Camh. Phil. Soc. 1845 ; Math. Papers, i. p. 75.
2 See pp. 164, etc.
ON OPTICAL THEOEIES. 169
rigidity. Thus we are compelled to treat the ether as an elastic solid of
very great — practically infinite — incompressibility. Now, the cubical
dilatation produced by a given state of strain is measured by e +/+ g, or
— + — + — , and the condition of incompressibility requires that this
dx dy dz
should be zero. It is not, however, admissible to omit the terms in
e+f+g in the equations, for they occur with the constant A as a factor,
and the physical condition that these terms should vanish implies also
that A should be very large. To obtain the correct equations we must
put
/ K DN ^du , dv , dw\
^^^UJ.+ di,^'d^)==^'
and they then become
4> + Bv%. . . . (18)
et cetera.
§ 4. MacCuUagh and Neumann omit the terras in p entirely from
their equations, both within the medium and over the surface, and are led
in consequence to erroneous results, though, as we shall see later, their
theories (modified so as to include the terms) have been developed by
Lord Rayleigh ' and Lorenz. Green, as we have seen, is perfectly con
sistent throughout ; but his final equations, unfortunately, are not con
firmed by experiment. If we assume the rigidity of the ether to be the
same in the two media, it is not difficult to show that Cauchy's surface
conditions are identical with those of Green, or, to be more accurate, that
Green's correct equations expressing the continuity of the stress and of
the displacement over the surface reduce to Cauchy's. Green obtains his
surface condition from the value of a certain integral over the surface ;
they may be obtained, perhaps more simply, from the equations of motion
of an element dS of the surface ; for, taking the case when the plane x=0 is
the bounding surface, let v be the thickness of the element, Nj, N/ the
stresses on it parallel to the axis of x, then we have
prdS'^^=(NyTS,')dS . . . (19)
Hence, when v is indefinitely decreased, N,=Ni', with other similar
equations. On Green's supposition that A^A,, B^Bj, these conditions
for Case I. (vibrations normal to the plane of incidence) lead to
div _dwi , " • • • . • • (^^)
dx dx
and for Case II. (vibrations in the plane of incidence) to
du dui dv dvi 't • • (^U
dx dx ^ dx dx' }
which are Cauchy's conditions. The difi'erence between the two theories
lies in their treatment of the waves of longitudinal displacement.
> See p. 189.
170 REPORT— 1885.
According to both Green and Cauchy they depend on a function 0,
where
,p = ,p^e ""'■'' + "'■'■''"> .... (22)
And in both theories
a'2 + &2 = ^ (23)
Green puts A/p very large, so that a'^ + h'^=0, and
(j) = ei''^IK sin (hj + ct) + Lcos (hij + ct)} . . (24)
while Cauchy, without any dynamical justification, writes A/^=— c^/P,
k being a large quantity, so that A is a small negative quantity. Hence
a'^ + b^= P.
The assumption of a negative value for A leads to the conclusion that
the modulus of compression is negative — that is, that the medium is such
that pressure causes it to expand and tension to contract, and this alone
is fatal to the theory.
§ 5. We come, then, to the conclusion that the phenomena of reflexion
and refraction cannot be explained, any more than the phenomena of
double refraction, on a purely elastic solid theory involving a sudden
change of properties on crossing the interface. Green's theory is the
only possible consistent one, and it, in its original form, leads to results
differing from experiment.
Part II, — Modern Developments of the Elastic Solid Theory.
We now come to the consideration of rather more modern investiga
tion on this subject. The limits of space will confine us to the theoretical
work which has been done. The great experimental researches of Fizeau,
Jamin, Quincke, Cornu, and others, will only be occasionally referred to.
A complete account of these must be left for some future time.
Chapter I. — General Properties op the Ether on the Elastic
Solid Theory.
The elastic solid theory of the propagation of light and double refrac
tion has been discussed in various papers by Haughton, Lame, St. Venant,
Boussinesq, Von Lang, Sarran, Lorenz, Rankine, Loi'd Rayleigh, Kirch
hoff, and others.
§ 1 . Haughton considered the problem of the general equations of an
elastic solid in a paper read before the Irish Academy in 1846, in which
he adopts Cauchy's views as to the constitution of the medium. These
views are modified in a second paper,' read in 1849, in which the general
equations are formed, and the correct expression found for the potential
energy.
In this paper Haughton shows how to calculate the strain in any
direction produced by a given elongation in the same direction. This
strain is proved to be inversely proportional to the fourth power of the
radius of a certain surface, called by Rankine the tasimonic surface. A
form is found for the equation to the surface of wave slowness, which is
said to reduce to MacCuUagh's if the vibi'ations be strictly transversal ;
but, in making the reduction, the dilatation is equated to zero, its co
' Haughton, ' On a Classification of Elastic Media and the Law of the Propaga
tion of Plane Waves through them,' Irish Trans, vol. xxii. p. 97.
ON OPTICAL THEORIES. 171
efficient remaining a finite quantity, and in conseqnence the results are
erroneous.
§ 2. Lame is the author of numerous papers, in the ' Comptes
Rendus ' and elsewhere, on the propagation of waves througli an elastic
medium, and his results are summed up in his ' Le9ons sur I'Elasticite.' ''
The general form of the equations for the strains are shown to contain
twelve constants, which become six if the dilatations be equated to zero,
and three when planes of symmetry are taken for the coordinate planes.
The equations of motion finally obtained may be written
W~'^'di! \dy~~dx) ~" 'Lh\Iir~ d^J ' • '< ^'
etc., which agree with MacCullagh's and with Green's if we omit the
terras involving the dilatation. The arguments to be advanced against
the theory are identical, then, with those which Professor Stokes has urged
against MacCullagh's.
§ 3, St. Venant has written many most important papers on the
subject of elasticity. He still adheres to Cauchy's theory and the form of
the equations of an elastic solid deduced from the hypothesis of direct
action between the molecules of the medium, and in his last great work
on the subject, the annotated French edition of Clebsch's ' Elasticity,'
states his reasons for so doing in §§ 11, 16. However, in the work he
employs Green's expression for the energy, with the twentyone co
efficients — ' Vu la controverse actuelle ou la majorite des avis est con
traire au notre.'
§ 4. In It paper printed in 1863 "^ he criticises Green's theory of double
refraction, arguing that Green's conditions for the tranversality of the
vibrations lead to isotropy. This conclusion is frequently repeated in St.
Venant's ^ papers, and it will therefore be well to investigate the point
somewhat closely.
Let us suppose that we have a simple elongation e in a direction
li, mj. 111, i^ ^ medium falfilling Green's conditions. Let I.2, mo, n^, I3,
TO3, ^3 be the direction cosines of two lines at right angles in a plane
normal to Z,, TOj, n^, and let us investigate the stresses N/, Ng', N3',
T/, T2', T3' on the faces of an element normal to these directions. Then
St. Venant's argument rests on the fact that N/ is independent of the
direction of the elongation, while Ta'and T3' vanish, and that this would
be the case in an isotropic medium. This last statement is of course
true, but on Green's theory Na'. ^3' ^o depend on the direction, which
they would not do in an isotropic medium, and T/ has a finite value,
while for an isotropic medium it would vanish.
The values for the stresses may be shown to be — 
1^2'= (iU2(LZ32MTO32 + ]^n32)}J
N3'={yu2(LZ2^jMm22iN„,22)}.l , . (2)
T/ = 2 {hlj3 + Mi».,m3 + Nnjng) e
T2' = T3' =
J Lame, Zegonit sur I'Elasticite. Paris : Gauthier Villars, 1866.
■^ St. Venant, 'Sur la distribution des elasticitSs autour de chaque point d'lm
solide,' LiouviWs Journal, S. ii. t. viii. p. 257.
3 See especially De St. Venaiit, 'Theorie des ondes lumineuses,' Aim. de Cldm.
S. IV. p. 22.
172 REPORT — 1885.
For an isotropic solid we should have Nj' = N3' =: (yu — 2L) e and
T/ = 0. Thus Green's medium in which the propagation of transverse
waves is possible has properties which distinguish it fi'om an isotropic
solid, for a simple elongation produces on any plane parallel to the direc
tion of the elongation a normal stress which depends on the position of the
plane, while it also produces shearing stress about an axis parallel to the
direction of the elongation ; and although the theory does not explain
double refraction satisfactorily, yet it is not open to De St. Venant's criti
cisms on this point.
§ 5 In the same jDaper St. Venant proposes a modification of Cauchy's
theory which leads to Fresnel's wave surface without any more conditions
than are required by Green ; for, putting in Green's expression,
AZ2 + Bm2 + 0^2 = X . . . . (3)
I, VI, n being the direction cosines of the wave normal, the equation to
■determine the velocity becomes —
{p V2  X  G/2  Hm2  Iw2} [(p V2  X)2  (p V* X)
{(M + N)Z2 + (N + L)m2 + (L + M) n^} + MNZ^ + NLjn^ j LM«2]
 {(H  L) (I  L)  (L + P)2} {GZ2 + Nto2 + M».2 + X  pV^} mhi"
 {(I M) (G  M)  (Mt Q)2} (NZ2 + Hm2 + Ln^ + X  pY''}nH'^
 {(G  N) (H  N)  (N + R^2} {MP + hw? + In"^ + X  pV^} Vm''
+ {(G  M) (H  N) (I  L) + (G  N) (H  L) (I  M)
2(LP)(M + Q)(N + R)}Z2»i%2 = (4)
And this will reduce to Fresnel's surface if A = B = C ; that is, if the
equilibrium stresses are equal, and the four conditions
(HL)(IL) = (L + P)2 X
(IM)(GM) = (M + Q)2
(G  N) (H  N) = (N h R)2 !" • (5)
(G  M) (H _ N) (I  L) + (G  N) (H  L) (I  M)
2(L + P)(MlQ)(N + R)=0
are satisfied.
These equations include those of Green's first theory, and are approxi
mately those which arise from what St. Venant calls an ellipsoidal
distribution of elasticities. Under certain circumstances the tasinomic
surface — which, it will be remembered, gives the tension in any direction
produced by a simple elongation in that direction — reduces to an ellipsoid,
and then the distribution of elastic constants is named by St. Venant
ellipsoidal. This distribution is produced when an isotropic medium is
unequally sti'ained in three perpendicular directions. The theory is
interesting, and important as showing that Fresnel's wave surface can
be deduced from the general elastic solid theory on other assumptions as
regards the constants than those given by Green, and that the vibrations
in this case are not necessarily in the wave front. There will, however,
in this case be a quasinormal wave, the velocity of which is given by the
equation
p72 _ X GZ2  Hm2  I/i2 = ;
ON OPTICAL THEOBIES.
173
and if Green's arguments as to the relative magnitude of the constants be
still supposed to hold, the quasinormal wave will disappear, and the
vibrations will be very neai'ly indeed transversal. The theory, however,
interesting as it is, does not enable us to overcome the difficulty of
reconciling the theories of double refraction and reflexion so long as we
adopt the view of Fresnel and Green, that the latter depends on difference
of density, not of rigidity, in the two media. It is also open to the
objection that if the medium be incompressible the displacements must
be in the wave front, and we must get in this case Green's conditions,
not the above ; while if the medium be not incompressible an appreciable
amount of energy must exist in the form of longitudinal vibrations.
§ 6. The question of the propagation of waves through an isotropic
medium, which is rendered anisotropic by the production of three elonga
tions, a, h, c, in three rectangular directions, has been studied by
Bonssinesq.^ The elastic constants are taken to be linear functions of
these permanent strains, and the number of constants involved in their
expression is reduced from the considerations involved in the symmetry
of the medium and the principle of the conservation of energy.
The equations of motion may be written
= (X + Va)'j? + (/z + pa)v
dx
■u
+ «T
{d'^u , T d^u ,
dy'
dH \
dx 1 dx dy dz .
(6).
with the condition implied by the principle of the conservation of energy
that \'= I', while if the normal stresses in the equilibrium condition
vanish a = p. These may be deduced fiom Green's equations by putting
A=((7p)a, B = ((Tp)&, C = ((r
py,
(7)
with similar expressions for the other constants, A and fi are the two
elastic constants of the nnstrained medium in the form in which they
are written by Lame, v/X and ^/(X + fx) being the velocities of trans
verse and normal waves respectively, the density being taken as unity.
_ _ It is thus shown that on the assumption that a, b, c are small quan
tities, such that their squares and products may be neglected, Fresnel's
wave surface is given if either u =0 or o = p. In fact, the condition «r =
leads to Fresnel's surface without any assumption as to the value of
a, h, c, for then the theory becomes identical with Green's second theory ;
while if (T=zp we have either St. Tenant's ellipsoidal condition or his
suggested modification of Cauchy, for to this degree of approximation the
two theories are identical.
Boussinesq, Liouville's Journal, S. ii. t. viii.
174
REPORT 1885.
"We may conclude, then, that Fresnel's laws as to double refraction
would hold in a medium strained in the manner Boussinesq considers,
but the theory as a whole is liable to the same criticisms as have been
made to Green's. Boussinesq is the author of another and different
theory, which we shall consider later, and which gives a better explana
tion of the phenomena.
§ 7. This same problem has been dealt with by Professor C. Niven,' who
has arrived at similar results without introducing considerations based
■on molecular reactions.
§ 8. The problem of double refraction has been treated in a different
manner by M. Sarrau, following up the suggestions of Cauchy as to the
nature of the ether in a crystal, aud his theory is developed in two papers
in ' Liouville's Journal.' In these papers^ the density of the ether in a
transparent medium is supposed to vary in a periodic manner from point
to point. The ether is arranged in concentric shells of variable den
sity round each matter molecule, and its density, variable round each
matter molecule, is the same at any one of a series of points situated
similarly with regard to the matter molecules. The ether is periodically
homogeneous, and the coefficients which occur in the elasticity equations
are no longer constant, but are peiiodic functions of the coordinates of
the point whose displacement is being considered ; from these equations
^are deduced a series of others with constant coefficients, containing the
;average displacements of the ether in an element of volume. It is to
•these average displacements that optical effects are supposed to be due.
Cauchy ^ has indicated the path to be followed in deducing these
auxiliary equations from the fundamental forms, and M. Sarrau arrives
.at the following conclusion.
If the fundamental equations be represented by
df" \dx' dy' ihJ ' ' V
^=«( • • ■)
?=H(. . . .).
dt
(8)
"Where F, G, H are functions v?ith periodic coefficients of u, v, w and
their differential coefficients, then the auxiliary equations will be —
d^u
= F' + G' + H'
(Py_ ^ Y" + G" + H" h
dt^
d^w ffi/// I n.'// I TT/'/
(9)
' C. Nlven, Quarterly Journal of Pure and Ajyplied Mathematics, No. .55, 1876.
* Sarrau, C. R. vol. Ix. p. 1174. ' Sur la propagation et la polarisation de lalumifere
•dans les cristaux,' Liouville's Journal, S. ii. t. xii. p. 1 ; t. xiii. p. 59.
' Cauchy, Comytes Jtendus, t. xxx. p. 17.
ON OPTICAL THEORIES. 175
F', F", F'" being symbolic functions obtained by substituting integral
functions of — , — ^ for the periodic coefficients of F, and similarly for
dx chf dz 'J
G', H'.
The second memoir ' is devoted to the consideration o£ the problem on
the supposition that the ether in a crystal is isotropic as regards its
elasticity, and that the variations in density are all which we have to
consider. Again following Cauchy, and treating the ether as a system of
attracting and repelling points, Sarrau arrives at the equations
<r=E(v> + r(v')}. . . . (10)
etc., where E and F are certain connected functions depending on the law
of force, and d the dilatation.
For free space —
E(v2)=ev2,
F(v2)=/,
e and / being constants.
For the ether in a crystal, omitting the consideration of dispersion, it
is shown that it is probable that E and F have the same forms, only
now e and / are periodic functions of the coordinates.
If we denote djdx, djdij, d/dz, djdt by a, /j, y, a, respectively, then
the equations in the crystal become, in conformity with the general rule,
«r%= V2(F,« + F,v + F3M;) + (/,« +/;/3 +/37)9,
etc., where F, G, H, etc., /, g, h, etc., denote now symbolic functions of
«, /3, y.
These general equations are simplified by the consideration of the
various kinds of symmetry possible, and it is shown that in the case of
ordinary biaxial crystals they reduce to
dho ,.„2 , .• M^
^'«_.„2 . (M
_=^v^. + ^,^, • • • • (11)
d'^w , , ^ dd
It is further assumed that f + fi ^= g + gi = h + h := 0. This, of
course, is the condition that the velocity of the normal wave should be
zero.
These equations are solved by putting M=:Pe*('^+'"2'+»^<"0, etc., and
lead to ■
_P__ Q _ R ^ (Fl+Qm + Rn),
whence
fl gm Tin
y^—f <^^ — g 0)2 — A
■' ■ "' +7^=0 • • . (12)
(li^—f w^ — g w^ — h
' Ziouville's Journa.!, Ser. ii. t. xiii. p. 69,
176 KEPOKT — 1885.
Thus the wave surface is Fresnel's. The direction of vibration, the ray
and the wave normal are shown to be in the same plane, but the direction
of vibration is at right angles to the ray instead of to the wave normal.
The assumed conditions / + j\ = 0, etc., form a serious objection to the
theory as it stands, but on this point it is capable of modification. The
vibrations, of course, are not strictly transversal within the crystal, but
I am not aware of any experiments which prove that they must be so.
Of course, if the medium be absolutely incompressible, the displacements
must be in the wave front, and the theory fails ; but the condition of
stability and the evanescence of the longitudinal wave require merely that
the incompressibility should be very great compared with the rigidity,
without being absolutely infinite.
§ 9. M. Sarrau has considered the peculiar phenomena presented by
quartz, and shows how on his theory the terms assumed by MacCullagh
will arise.
For the crystalline symmetry of such a body, the equations are shown
to take the form —
dt^ •' \ dxj •" Kdij dzj
d^v /„, dd\ . „2 /' <^^' , <^w^
d^w /„o dd\ , „2 /' t^^ I <i'"\
i
(13)
and it follows that two elliptically polarised waves can traverse the
medium in any given direction.
The velocities of these waves are given by
'=f7(://)sinM ±l^{(sr_/)2sin4
+ }^ (g.cos'^d + f.sm^O) x(g,cos^eg,sm^d)^ . (14)
fy and gf, are two constants which are probably very small, and, in that case,
the squares of the principal velocities at right angles to the axis are/
and g, while the squares of the velocities parallel to the axis are given by
If pi represent the ratio of the axes of the ellipse in the ordinary wave,
P2 that in the extraordinary, then
q^ cos^ fl — 9 1 sin^ ,, r\
^"'^■^2Cos=^a + /,sin^0 • • • ^^^^
The major axis of the extraordinary ellipse is perpendicular to the prin
cipal plane, that of the ordinary ellipse is in the principal plane, while the
two waves are polarised in opposite senses.
§ 10. De St. Venant ' criticises the theory in the following points, p being
the only periodic variable, the equations, he argues, should be treated as if the
' St. Venant, ' Sur les diverses mani^res de presenter la theorie des ondes Inmi
neuses,' Ann. de Chim. (4), t. xxv. p. 335.
ON OPTICAL THEOKIES. 177
periodic coefficient Tvas attached to the first term, p — —^ etc., and he states
that the development of the equations p = . . . . leads to different
results. Sarrau,' in reply, points out that this depends on the relative
magnitudes of the quantities a, ft, y, a^, and the other parameters ; on
making the same suppositions in the two cases the results, he shows, are
identical. One may, however, start from the general equations of an elastic
solid with two coefHcients, and, by supposing the coefficients to be periodic,
arrive at the general equations already found.
M. de St. Venant finds a difficulty in explaining dispersion, for in an
isotropic medium the periodicity of the coefficients vanishes. This may
be true, and yet the equations contain differential coefficients above the
second.
§ 11. The theory advanced by Von Lang ^ might perhaps more strictly
be considered under the next section : ' Theories based on the mutual
action between matter and the ether.' The theory is, however, so slioht
a modification of the ordinary elastic solid theory that it will be more
convenient to deal with it now.
Von Lang supposes that the displacements which come into the
ordinary elastic solid theoiy are displacements of the ether relative
to the molecules of the matter. He assumes that the ratio of the
matter displacement to that of the ether is in general a function of the
direction, but that for three directions we may write
U=a2^t, V=i2y, W=c2m;,
U, V, "W being displacements of matter, «, v, w of ether.
He then forms the equations of motion, and, equating the velocity of
the quasilongitudinal wave to zero, arrives at Fresnel's wave surface.
The theory cannot be regarded as having any real physical signification,
for the elastic forces produced in the ether will depend on the real dis
placements of the ether particles, not on the displacements relatively to
the matter, and the velocity of the normal wave cannot vanish, for if it
does the medium becomes unstable.
§ 12. Von Lang ^ has also given a theory of circular polarisation,
which consists in adding to the ordinary equations terms such as
.2 fdv _ dw\
\dz dyj'
From this it follows that the velocity in a medium such as sugar is
g^ven by
'Ztv a
L being the wave length in air ; while in quartz
0,2 = a2 _ «l_^8in20 ± 1 / I (^2 _ ,2)2 8in49
j^^cos^flj . (16)
Sarrau, ' Observations relatives k I'analyse faite par M. de St. Veuant,' Ann de
Chim. (4), t. xxvii. p. 266.
^ Von Lang, ' Zur Theorie der DoppelBrechnng,' Wied. Ann. t. clix. p. 168.
' Von Lang, ' Zur Theorie der Circular Polarisation,' Pogg. A?m. t. cxix. p. 74.
1885. ^
178 REPORT— 1885.
Von Lang holds that the experimental law connecting the rotation
and the wave length is
h'
Rotation ^h + \ . . . .
and this is given by the above expressions if
a2 = m + + . . . .
P = rh + ;' f
s
L
No reason is given for assuming the form 2^^^ •— — —  j rather than
A
that selected by MacCuUagh, o^f ^ — ^ ), which leads to the correct
relation between the rotation and the wave length without any violent
supposition as to the form of o^, such as is made by Von Lang ; and,
though neither theory has any mechanical basis, this fact alone is suffi
cient to render MacCullagb's the more probable, while experiments on
the size of the rings produced when convergent polarised light is trans
mitted through a plate of quartz cut at right angles to the axis agree
rather better with MacCuUagh's form than with Von Lang's.
§ 13. Another theory of double refraction was developed by Lord
Rayleigh ' in 1871. It had been suggested originally by Rankine,^ and
Stokes in his British Association Report referred to it, and showed that in
its original form it was untenable. The theory is also given by Boussinesq
in a paper in ' Liouville's Journal,' ^ which will be considered in full under
the next section.
Lord Rayleigh points out the inconsistency already referred to be
tween the theories of double refraction and reflexion given by both Green
and Cauchy, while, as we shall see when considering the polarisation
phenomena accompanying the reflexion, difl"raction, and scattering of
light, he believes that Neumann and MacCullagh, though consistent,
were wrong throughout. He then remarks that the analogy of a solid
moving in a fluid would suggest that the first effect of the matter mole
cules in a transparent body would be to alter the apparent density of the
solid, and that conceivably this alteration might depend on the direction
of vibration. He supposes that the statical properties of the ether are
not altered by the presence of the matter, and the equations of motion
may be written
d'^U dp , n^o
I
d^v dp , D„o
P — s =  + B V"^«
^vdf dy
dlV dp , r,„y
^T/2 = 7 + ^^ "^
where p is written for A?, c being the dilatation.
' Hon. J. W. Strutt, ' On Double Kefraction,' Pkil. Mag. June 1871.
^ Kankine, Phil. 3Iag. June, 1851. ' See p. 215.
(17)
ON OPTICAL THEORIES. 179
Lord Rayleigh further assumes the medium to be absohitely incom
pressible, so that c is zero and A is infinitely large, p remaining finite ;
this, of course, leads to the fourth equation —
du , dv , dw n
^T + ^ + ^ = ^ .... (18)
And from these equations the equation to the surface of wave slowness is
shown to be
— 1 ^1 _l
a2 h^ c^
This, however, is not Fresnel's surface, and experiments of a very
high ' degree of accuracy have shown that the wave surface in a
•crystal is very approximately indeed Fresnel's surface, and of course
this is fatal. But, as we shall see in the next section, according to all the
theories yet proposed based on the mutual reaction between matter and
•ether, the first and most important effect of the matter is to alter the
apparent density of the ether in the way here supposed. The mutual
72
reaction, it can be shown, will introduce terms of the form Jc —^ into the
dt^
equations, and k may conceivably depend on the direction.
§ 14. Equations of motion practically the same as Lord Rayleigh's
are given by Boussinesq, Lommel, Ketteler, and Voigt, and the question
arises. Are these equations incompatible with Fresnel's wave surface ?
Lord Rayleigh has, of course, proved that they are if the equation
du dv div ^
dx dy dz
•expresses an absolutely necessary condition ; but it is not difficult to show
that if, instead of the above equation, we put
1 ^w J. (^ 1 du „
a^ di b^ d^ '^ dz ~ ' ' ' ^ ^
then the wave surface will be Fresnel's, the direction of vibration will be
normal to the ray, and will be in the plane containing the ray, the wave
normal, and an axis of the section of the ellipsoid a^x"^ + I'^if + c^^^ = i
by the wave front, and while the velocity of propagation will be inversely
proportional to the length of this axis.
Assuming equations of the same form as Lord Rayleigh's (17), we have
to determine the pressural wave given by p —p^ti(ix+my+nz\e) ^.j^g equation
■where ti = \Q^^Klx+my + ,izYl), gtg_^
and this, on Lord Rayleigh's assumption of Ik + mu + wr = 0, reduces to
Po = «B0oV^{^, + ^^ + ^y} . . . (21)
• See Stokes, Proc. Roy. Soc. vol. sx. p. 44B ; Abria, Ann... de Chhnie; Glazebrook
riitl. Trans. Pt. I. 1879 ; Kohlrausch, Wied. Ann. t. vi. p. 86 ; t. vii. p. 427.
n2
180 REPORT — 1885.
while, on the hypothesis suggested above, we should find
po=iBdQ{\l + lum + rn} .... (22)
The theory as here modified would, it appears to me, agree in its results
with all the experimental facts ; the main difiiculty lies in the assumption
of equations of the form—. — =— ^ + V ^u for the medium when it is not
^ a''' at B ax
strictly incompressible. The value of 2^ is generally A— + = +_— j,
and the introduction of « is based on the supposition that  —  + 
ax ay dz
is zero, and A infinite ; it is questionable if the substitution ought to be
made, except in this case.
§ 15. Kirchhoff 's paper on double refraction ' was read before the
Royal Academy of Berlin, and is contained in their ' Transactions ; ' its
more important part deals with the problem of reflexion and refraction.
So far as the double refraction is concerned, it does not differ in any
important points from Neumann's theory. The medium is supposed to be
incompressible, so that { — + —  vanishes, but the coefficient of this
ax ay dz
expression is treated as finite, and the terms involving it in the ex
pi'ession for the energy are omitted. The criticisms on Neumann's theory,
contained in Professor Stokes's report, apply again here.
Chapter II. — Dispersion of Light.
In 1870 Ketteler ^ published a paper on dispersion, which forms the
first of his important series on that subject. He commences with an
account of Cauchy's theory and the various modifications which have
been proposed.
§ 1. Redtenbacker ^ had considered the problem under the supposition
that each matter molecule is surrounded by an ether shell, and obtained
the formula
J = a+^+c\2 (23)
\ being the wave length in the medium, and /x the refractive index.
§ 2. Christoffel,^ discussing Cauchy's formula, already mentioned,' viz.
1 ^ i ^
had shown that, while a and h may be considerable in value, the
other constants decrease rapidly. This twoconstant formula may be
written —
/^= ., ■ /°^^.. r. • • . (24)
I
I
v/0^")V('x')'
' Kirchhoff, Ahhandl. der Konigl. Ahid. zu Berlin, 1876.
2 Ketteler, ' On the Influence of Ponderable Molecules on the Dispersion of Light,
and the Signification of the Constants of the Dispersion Formulae,' Poffff. Ann,
t. cxl. p. 1.
^ Kedtenbacker, Bi/namidenSi/stem, Mannheim, 1857.
■• ChristofEel, Fogg. Ann. t. csvii. * See p. 165.
ON OPTICAL THEORIES. 181
Thus /uq and Xq are the refractive index and wave length for the shortest
waves transmitted, and /itov/^the refractive index for the largest possible
waves.
§ 3. The various theories are then compared with experiment, by
Ketteler, and it is shown that the formula
i,=KX>+A + g^.O .... (25)
represents the results of the comparison most accurately. This formula
was obtained by Briot, working on the same lines as Redtenbacker, but he
supposes the coefficient K, which he shows depends on the direct action
between matter and ether, to vanish. Van der WilHgen ' also called
attention to the importance of the term in X^, but could not account for
its existence. Ketteler, following Briot, then analyses the manner in
which these various terms arise, and shows that the force on any
vibrating ether particle may be written
X2
< Displacement of particle >
x{(, + /0(lL)^%f+^X^}
This, of course, gives
l=A + g + KX2 (26)
The term in g + h arises from the mutual reactions of the ether particles,
supposed to be uniformly distributed. If the action of the matter be
simply to produce a periodic variation in the density of the ether, the
terms in L and M are introduced, while the term involving gi + h^
comes from a direct force expressed by mm^rf^{r) between the ether
and matter particles wi and wij respectively. If we put rf^(r) = n/r",
then the value of gi + 7i, is —^(n — 2)'Sim^fi/r"'^^.
Briot supposes that the term KX^, to which this gives rise, is not
requixed by the experimental results, and therefore puts w=2. Ketteler,
however, shows that this term must be included.
Holtzmann and C. Neumann had already insisted on the importance
of retaining in the equations terms to express this direct action, and
Neumann gives as the expression in an isotropic medium for the force
arising from a displacement ti,
Cu + C ^ + C" i^.
But the theory of dispersion in its complete form requires that thu
motion of the matter particles should also be included. This is treated
of in the next section of the Report.^
A problem closely connected with dispersion is the relation between
the refractive index and the density of a medium. This has been dealt
with experimentally by various physicists, notably by Gladstone and Dale
in England, and Ketteler in Germany.
§ 4. L. Lorenz ^ has recently developed the theory of the transmission
' Van der Willigen, Archives du Muue Teyler.  See p. 213, etc.
^ L. Lorenz, ' On the Refraction Constant,' WieA. Ann. t. xi.
182 KEPOBT— 188/5.
of light through a medium consisting of a series of small spheres im
bedded in the ether. The velocity of light in the interspaces is the same
as in free space, and the wave length is supposed to be great compared
with the intei'molecular distances. It is assumed, then, that the disturb
ance u at any point may be written u= (t(Q + u<,)C + UiS, where the
average values of 1*1 and «.> over the space containing some considerable
number of molecules are zero, and C and S are written for the sine and
cosine of kt — Ix — mij — nz — c. From this it follows that, if /z be the refrac
tive index and d the density,  ^ — _ is proportional to d.*
The paper is followed by one by Lorenz and K. Prytz, giving the
results of an elaborate series of observations which show a close agree
ment between this expression and experiment.
Chapter III. — Aberration and Phenomena connected with the Motion
OP THE Medium through which Light is being propagated.
§ 1. The aberration of light on the undulatory theory was accounted
for by Fresnel • on the supposition that a moving body of refractive
index fi carries with it a quantity of ether of density fi^ — l, the density in
a vacuum being unity, while light is propagated through this ether, part
of which is at rest and part mo^ang with a velocity v (that of the body),
as if the whole were moving with the velocity (I— /i~')t;.
The experiments of Fizeau^ on the displacement of the fringes of
interference by a moving medium led to a result in close accordance with
this theory,
§ 2. A more general and simpler proof than the one published by
Fresnel of the fact that this leads to the ordinary laws of reflexion and
refraction was given by Professor Stokes in 1846.^
In this paper Professor Stokes points out that the same result as to
the velocity of light in the medium will be arrived at if we suppose the
ether on entering the medium to be condensed, and on leaving it to be
rarified, while the whole ether in the body travels with the velocity given
above ; for, if we take two planes, one outside the other inside themedium^
each moving with the A^elocity v normal to itself, the quantity of ether
which crosses the two planes per unit time will be the same, and hence,
if V be the velocity of the ether in the medium, then we have, since the
densities are 1 and fi^ respectively,
and hence Y M^""'
Moreover, this comes to the same thing as supposing the medium to be at
rest, while the ether outside moves with a velocity v, and that inside
with a velocity?;/^. The direction of a ray is shown to be that in which
the same jDortion of a wave moves, moving relatively to the medium, and is
found by drawing from a given point a line of length V//i in a direction
* Compare this with a similar paper by H. A. Lorenz, p. 255.
' Fresnel, Anvales de Chimie, t. ix. p. 57.
 Fizeau, Annates de Chimie (3), t. Ivii. p. 385.
' Stokes, ' On Fresnel's Theory of the Aberration of Light,' Phil. Mag. vol. xxviii.
p. 76; Afatheviatical Pajjcrs, vol. i. p. 141.
ON OPTICAL THEOEIES. 183
normal to the wave, and from the extremity of this line a second of length
v/f.i^ in the direction of motion of the ether; the ray is the line joinino
the first point to the extremity of this second line. The velocity of the
ether is resolved into its components perpendicular and parallel to the
reflecting sui'face, and the effect of each component is considered ; it
is shown that rays are reflected and refracted according to the ordinary
law of sines.
§ 3. But in a paper six months previously Professor Stokes ' had
considered the problem in a much more general manner. He supposes
that the earth and planets carry with them a portion of the ether sur
rounding them, so that close to their surfaces the ether is relatively at
rest, while the velocity alters as we recede from the surfaces until, at no
great distance, it is at rest in space.
The direction in which a body is seen is normal to the waves which
have reached the observer from the body, and the change in this apparent
direction which arises from the motion of the ether is investigated.
The axis of z is taken in the direction of the normal to the undisturbed
wave, and a, f3, y are the angles which the normal to the actual wave
makes with the axes ; u, v, w are the velocities of the ether at a point
X, y, z at time t ; V the velocity of light. The equation to the wave is
^ = C + Vi + c,
i being a small function of x, y and t.
Then, by considering the displacement of the extremity of an element
Ylt, drawn normal to the wave, it is shown that at time t + Zt the equa
tion is
z = G + Yt + ^ + {lo + Y) dt,
and hence we see that
dZ_
, w.
At
From this we find
If now
IT 1 [dw 7 ,T TT 1 [dw ,
dio du dw dv
dx dz dy dz
so that udx + vdy + wdz is a complete differential, then
«2 — "l = "vT > P2 — P\ =
w.,zt, ; _ T _ ^'2  ^1
and these equations, it is easily seen, imply the known law of aberration.
In an additional note it is shown that if aj, /3i be the inclinations of
a ray at any time to the axes, then
fdiij dw\ . \
^^^=\jz'd^Y'
j,i f dv dw \ T.
\az ay J
(27)
' Stokes, 'On the Aberration of Light,' Phil. May. vol. xxvii. p. 9 (July, 1845) •
Mathematical Pampers, vol. i. p. 134. '
184 KEPOBT— 1.S85.
So that, i{ vdx + vdy + ivclz be a comjDlete differential, Jctj and dj3i both
vanish, and the path of the ray is a straight line.
Thus, if the motion of the ether produced by the passage of the trans
parent medium through it have a velocity potential, all the phenomena
of aberration will be such as are actually observed. The important ques
tion as to whether such a motion is probable in the ether is discussed in
another paper. •
§ 4. Professor Stokes's views on the constitution of the ether are given
in his wellknown paper on fluid friction.^ He distinguishes there between
the properties of rigidity and plasticity, pointing out that an elastic solid
may under different external conditions become a viscous fluid, while
the gradation between viscous and perfect fluids is quite regular. There
seems, then, a probability that the property of rigidity will run to some
extent through the whole series, becoming, in the case of fluids, masked
by some other more important property. The mobility of a fluid is the
limiting case of great plasticity ; but even a perfect fluid may admit of
a finite, though extremely small, amount of constraint of the nature of
shearing stress before being relieved from its state of strain by its mole
cules assuming new positions of equilibrium. A consideration of the
length of a wave in light motion — about '00003 inches — renders it pro
bable that ' the relative displacement of the ether particles may be so small
as not to reach, or even come near, the greatest relative displacement
which could exist without the molecules of the medium assuming new
positions of equilibrium.'
These same views also tend to confirm the belief that for fluids, and
among them the ether, the ratio of A to B (the elastic constants of the
medium in Green's notation) will be extremely great.
We are led, then, to conclude that, in considering the motion set up
in the ether by a moving body such as the earth, we may treat the
ether as an incompressible fluid, while, on the other hand, when
dealing with the extremely small disturbance produced by the passage of
a lightwave the rigidity of the ether may come into consideration, and
the equations required will be those of an elastic solid. In the first case
any tangential forces which may arise, if the fluidity be not perfect, will
depend on the relative velocities of the parts of the fluid ; in the second
case such tangential forces will depend on the relative displacements of
those parts. In the paper in the ' Philosophical Magazine ' for 1846
Professor Stokes shows that it is probable that a velocity potential will
exist unless the action of the air on the ether be such as to prevent it,
and, further, that it is improbable that the air will so act.
For suppose a sphere started from rest in such a medium, and then
after a short interval stopped for a time, then started, and so on .
The initial motion will have a velocity potential, and if the fluid
were perfect this would continue, so that reducing the sphere to rest
would stop the motion everywhere. But the motion with the velocity
potential is shown to be unstable, and hence there is left in the neigh
bourhood of the sphere a small outstanding disturbance. This is carried
' Stokes, ' On the Constitution of tlie Luminiferous Ether viewed with reference
to the Phenomenon of the Aberration of Liglit,' Phil. Mag. vol. xxix. p. 6 ; Math, aiid
Phys. Papers, i. p. 15.3.
* Stokes, ' On the Theories of the Internal Friction of Fluids in Motion, and the
Equilibrium and Motion of Elastic Solids,' Trans. Cavib. Phil. Soc. vol. viii. p. 287;
MatJi. and Phys. Papers, i. p. 75.
ON OPTICAL THEORIES. 185
off with the velocity of light, which is about 10,000 times as great as
that of the earth, so that at the end of the second interval the ether near
the sphere is at rest again and the same effect is repeated. It seems,
therefore, probable that there will be a tendency to set up a motion in
the ether not having a velocity potential, but that the beginnings of such
motion will be propagated away into space at a very great rate, and that
the actual motion will satisfy the condition that udx + vdy + wdz is an
exact differential.
In a subsequent paper Professor Stokes gives the solution of the
equations of motion of a sphere moving in a viscous fluid, and then
proves that when the fluid becomes perfect the motion becomes unstable,
so that udx+vdy + xodz is not a complete differential ; but if the tangential
force depends, not on the relative velocities, but on the relative displace
ments of the molecules — that is, if for the beginnings of the variation from
irrotational motion we must consider the rigidity of the ether (?".e , in
our mathematics use the equations of an elastic solid) — then, as shown
already, this nascent variation from irrotational motion will be propagated
away by transverse vibrations, which, however, do not produce optical
effects, either because they are too feeble or because they are discon
tinuous, or, if continuous, because their period falls outside that of the
visible spectrum.
Or, to put it slightly diffeiently, if the fluid has any very slight
rigidity, a given arrangement of its parts is not necessarily one of equi
librium. Suppose, then, the fluid displaced from rest by the sudden
motion of the solid, and that after a short interval the solid is stopped,
the velocity of the fluid will be reduced everywhere to zero, but the
resulting configuration will not necessarily be one of equilibrium, and the
motion arising from this slight strain will be set up.
Thus, without making Fresnel's somewhat violent assumptions as
to the relation between the ether within and without a transparent body,
a perfectly reasonable and consistent account can be given of aberration
depending only on the irrotational character of the motion induced by the
moving body in the surrounding fluid. Unfortunately, as Professor Stokes
points out, we have as yet no experiments competent to decide between
the two, and he does not see how such experiments could be devised.
§ 5. Ketteler is the author of a long series of papers connected with
the subject of aberration, which have appeared in Poggendorff's ' Annalen.'
The last of these ' contains a summary of the results of the whole.
The problem of reflexion and refraction at a moving surface is con
sidered, and it is shown that the intensities of the reflected and refracted
rays will not be modified by the motion if the vibrations be at right
angles to the plane of polarisation, as Fresnel supposed.
§ 6. The papers also deal with the problem of the emission of light
from a moving source, and the principle first enunciated by Doppler,^ in
consequence of which it follows that if the source and receptacle approach
each other in time ^ by a space equal to n times the wave length in the
medium between the two, then the receptacle receives in that time n
more vibrations than it would if the two were relatively at rest ; and if
this number be N, the apparent frequency is increased in the ratio N ) «.
' Ketteler, ' Ueber den Einfluss der astronomischen Bewegungen auf die optisch n
Erscheinungen,' Pt. VI., Pogg. A^m. t. cxlvii.
^ Doppler, Lasfarhige Licht der Dojjpel Sterne. 1842.
186 EEPOBT— 1885.
to N, or if V be the velocity of light, v that of the source towards the
receptacle, in the ratio Y + v to V.
This principle has been considered by other writers, among them
Petzval, Von Ettingshausen, Klinkerfuess,' Van der Willigen,^ and
Seccbi,^ and an interesting discussion of their work has been lately
given by H. H. Turner, in a dissertation for a fellowship at Trinity
College, Cambridge.
Chapter IV. — Reflexion and Refraction.
§ 1. The various theories of reflexion and refraction advanced by
Fresnel, Green, MacCullagh, Neumann, and Cauchy have been discussed
by several writers, and attempts have been made to reconcile them with
the experiments of Jamin, Quincke, and others. Jamin was the first to
show that by reflexion at most transparent media plane polarised light
becomes elliptically polarised, and that this elliptic polarisation is most
marked when the angle of incidence does not difier much from tan '//.
Moreover, for some substances for which the refractive index is greater
than 14 the phase of the component in the plane of incidence is re
tarded relatively to that at right angles to the plane, while if the index be
less than 1'4 the reverse is the case.
The original theories of Fresnel and MacCullagh do not in any way
explain this phenomenon, and are therefore incomplete.
§ 2. Cornu'* has discussed the application of Fresnel's theory
to crystals, and has suggested a means of explaining the apparent
discontinuity of the displacement normal to the surface to which that
theory leads. The explanation— which Professor Stokes has been in
the habit of giving, independently of Corna, in his lectures at Cambridge —
rests on the fact that the density of the ether is different in the two media.
If, then, we take two planes in the two media parallel to the interface
and at a small distance apart, the quantity of ether between the two
planes remains the same ; hence, if u, u' be the displacements normal to the
planes, and p, p' the densities, the equation of continuity gives pu= p'v! ,
and this is the condition assumed by Cornu in his papers. This con
dition, combined with those of the continuity of the displacement parallel
to the surface, is consistent with the equation expressing the conservation
of energy.
The correctness of this condition depends on the view we take of the
ether in the two contiguous media. If the two portions of ether be
treated as two separate elastic solids in contact over a common surface,
then over that surface the displacement must be the same in the two
media ; but the equality of the displacement normal to the surface cannot
extend beyond a very small distance within the medium, and in the dis
placement is included that which comes from the pressural wave, as well
as that which produces light. During the motion, of course, the bounding
surface of the two media does not remain plane, but is a curved surface,,
the coordinates of any point on which at time i are w, y + i/, w + z.
' Klinkerfuess, Astronomische Kachrichten, t. Ixv. p. 17, t. Isvi. p. 337.
"^ Van der Willigen, Archives du Musee Teijler, t. iii. p. 306.
' Secchi, C. R. t. Ixxxii. p. 761, t. Ixsxiii. p. 117.
* Cornu, ' Eecherches sur la reflexion crystalline,' Ann. de Chim. (4), t. xi.
p. 283.
ON OPTICAL THEOKIES. 187
The condition of no dilatation holds throughout both media, and the
stresses over the surface are the same in the two.
According to this view, a small portion of ether which belongs to one
of the two media remains of unchanged density, and always forms part
of the same medium.
We may, however, consider the question somewhat differently, and look
upon the ether in the two media as continuous, but of different densities
on the two sides of the interface. A portion of ether belonging to the
first medium may cross the interface and become part of the second, and
in so doing its density is changed. There will thus be a thin sheet of
ether lying over the interface in which rapid periodic changes of density
are occurring.
If, then, we consider the motion on the two sides of the sheet, we
have for its determination the fact that the quantity of matter within the
sheet is constant, and therefore that puz=zf)'u\ while the motion parallel to
this sheet will ultimately be the same in the two media, and the energy
in the reflected and refracted waves will be equal to that in the incident.
But this condition pu=p'u' does not hold within the sheet where the
variations of density are taking place, and where the effects of the
pressural wave are appreciable. The motions denoted by m and u' are
lightmotions, exclusive of those which give rise solely to the pressural
wave. Moreover, it is supposed that this layer of variable density is so'
thin that the phase of the distuibance may be treated as the same over
its two bounding surfaces. It is further assumed that the above are the
only conditions which hold at the surface, and these can be satisfied
without supposing any change of phase to arise from the reflexion. As a
fact, there are other conditions involved in the equality of the stresses
over the surface, and to satisfy these it is necessary to suppose that when
the vibrations are in the plane of incidence the phases of the incident
reflected and refracted waves difier even at the surface.
To assume Fresnel's conditions, as is done by Cornu, without change
of phase is equivalent to supposing that this sheet of variable density is
indefinitely thin when compared with the wave length of light.
Green himself considered the effect of supposing tlie change in
refractive index to take place in a gradual manner, replacing the refract
ing surface by a regular series of layers, of indices Hu fx^, etc., each of
thickness t ; and proved that the effect of such a series would be to make
the intensity of the reflected wave more nearly that given by Fresnel's
tangent formula.
The effects of supposing the change of properties from one medium to
the other to be gradual was discussed by L. Lorenz in the year 1860.
§ 3. In his first paper • he supposes that Fresnel's formute express
the result of a sudden transition, and investigates how they must be
modified if the transition be gradual. The variable sheet is divided into
a series of layers, each of constant density. A ray reflected at one of the
interior layers will on emergence be retarded relatively to the ray
reflected at the surface. Let I be the retardation of the ray reflected at
a layer on which the angle of incidence is x, and let a, ft be the angles of
incidence and emergence, then the disturbances in the reflected ray are
shown to be : —
,r j^; ^o^^'^^' ' On the Eeflexion of Light at the Bounding Surface of two Isotropic
Media,' Pogg. A^m. t. cxi. p. 460. ^
188 REPORT — 1885.
(1) Light polarised in the plane of incidence —
R = A s^" ("  /^) fcos kt + tan A sin ht\ . . (28)
sin(a + /3)L J
where
. sin O cos a P/ o n i. ■ o , , \dS , /nrw
tan A = r75 .  , ( COS'' p tan a; — sin p cot j; )dx . (29)
sm'' a — sm^ p}a\ J dx
(2) Light polarised at right angles to the plane of incidence —
R' =  A' ta n (a  ft ) V^^ ^^ + tan A ' sin kt\ . (30)
tan (a + /5) L J
2a sin 2/3 f^r sin 2x _ sin 2ft~\dc . .oi >,
a  sin2"2/3jl "^1^2/3 '^^^x \ dx ' ^^
where
, , , sin 2fi
tan A' =^20
7^
Now  is always small, hence A is small ; but for sin 2a = sin 2/3,
ax
or tan a = ft, tan A ' is infinite.
Jamin's results as to positive and negative reflexion are shown to
follow, and if it be assumed that the density is approximately proportional
to/ii* — 1, the thickness of the variable sheet can be estimated, and is found
to lie between ^L and j^^ of the wave length.
In criticising this theory. Lord Rayleigh, in a paper we shall shortly
consider, has pointed out that Fresnel's tangent formula does not express
the result of sudden transition, and that Green's formula, which does,
deviates from the truth on the other side. On the electromagnetic
theory, however, the tangent formula is strictly true, and Lorenz's
investigations regain their interest.
Another objection which Lord Rayleigh has made to the supposition
of gradual transition, however, may be a serious one. It is that there
should be some indication of colour in the light reflected near the polaris
ing angle, since it is to all intents and purposes a case of interference
produced by a thin plate. It may, however, happen that the thickness of
the plate is comparable with that of the black spot in Newton's rings,
and so, though big enough to modify the quantity of light reflected, is too
small to show colour. According to Newton, the thickness of the black
spot in a soap film is about Jo of a wave length, while Reinold and
Riicker have recently determined it as g^^, and these fall within the
limits required by Lorenz to explain the variations from Fresnel's tangent
formula.
In another paper ' the problem of reflexion at a surface across which
the density varies gradually has been more fully considered by Lorenz,
and the surface conditions on either side of the variable layer are deduced
according to a strict elastic solid theory, and lead to similar conclusions.
§ 4. Cauchy gave the results of his theory of reflexion and refraction
without the calculations which were supplied by Briot * in France, and
Beer ^ and Eisenlohr '' in Germany.
' L. Lorenz, Poffg. Ann. t. cxiv. p. 238.
'^ Briot, LiomiUe's Journal, t. xi. p. 305 ; t. xii. p. 185.
' Beer, Fogg. Ann. t. xci. and xcii.
* Eisenlohr, Fogg. Ann. t. civ. p. 346.
ON OPTICAL THEORIES. 189
An account of the various theories is also given iu papers by Lord
Rayleigb,' with a careful criticism and comparison of them all.
In the first part of this paper Lord Rayleigh discusses fully the
difference between the theories of Green and MacCullagh, and develops
completely the consequences of the latter, taking into account the full
effect of the pressural wave. This had been done first by Lorenz in the
paper already referred to, and he showed that the results to which
MacCuUagh's theory leads are totally inconsistent with experiment.
Lord Rayleigh points out that the fundamental assumptions of Green
and Fresnel amount to assuming an identity between the statical pro
perties of the two media, while the dynamical pioperties depending on
variation of density are different ; while, moreover, as we have seen
already, Cauchy's surface conditions, founded on the principle of the
continuity of the displacements and their differential coefficients with
reference to the normal, though erroneous if we suppose the rigidity of
the ether different in the two media, become identical with Green's if
we adopt his fundamental hypothesis. The real difference between Green
and Cauchy lies in their respective treatments of the pressural waves.
The true surface conditions lead to the folio wins: results : —
Let I, T], i^ be the displacements, n the rigidity, m the second
coefficient, such that m + n is the A of Green's papers, and D the
density, while g^ = (m + n) jD, y = ?i/D for the one medium.
Let a; = be the bounding surface, and let the axis of z be parallel to
the front of the waves. And suppose/, F, and/i to represent the incident
reflected and refracted waves, while f and ((>' are the angles of incidence
and refraction.
Then, for vibrations normal to the plane of incidence —
tan f' n'\
F' tan (p n
(32)
f tan (p' i
tan <i> 1
and this becomes : —
Case I. n = n' (Green, Fresnel, Cauchy) —
F^ _ sin (f  f)
f 8in(f + ^) • • • • ^'i^)
Case II D = D' (MacCullagh, Neumann)—
F_ tan((^^0)
/ tan (f + ^) • • • • ^''*^
Now, Jamin, Quincke, and others have shown that this latter formula
is not strictly true, and hence at this point the evidence is already in
favour of Fresnel's hypothesis.
Turning now to the case of the vibrations in the plane of incidence, put.
dx dij
_ d^_d'^
dy dx
' J. W. Strutt, ' On the Reflexion of Light from Transparent Matter,' Phil. Mag.
August 1871 ; ' On the Reflexion and Refraction of Light by Intensely Opaque
Matter,' Phil. Maj. May, 1872 o j j f"^
(35)
190 REPORT — 1885.
Then ^ refers to tlie light wave and $ to the pressural wave ; let *'
refer to the incident wave, *" to the reflected, ^, to the refracted, so that
Tlr __ \p'gHa.T + l!i + cO r ijf//gt(ax + 6i/ + ct)
etc. Then the surface conditions become in general, if we put
^/ ^ y^U _ X, ^'  ^" = Y.
i(«> + a)!) =*i  X
6(* — <I>i) = aY — a,^i
4.{m(a'2 + i^)  ^nb^} + ^nabY
=<I)i {)«'(ai'2 + ^2) _ 2n'b''} + 2n'a,b^i . . (36)
n{b''^i a^X + i&(«Y  «,^,)}
= «' {^^X  a, 24', + ^•Z;(«Y  a,^,)} • • (37)
MacCullagh, in his original work, neglects the pressural waves en
tirely, and pats $ = <t, = 0, dei'iving his result (Fresnel's sine formula)
from equation (35). These results are inconsistent with (36) and (37),
and therefore wrong. To obtain the correct solution we must remember
that m is infinitely great, while a'^ + h^ is vanishingly small, and m(a'^ + b^)
= Dc^. This is what has been done by Green, and applied by Lorenz
and Lord Rayleigh to MacCullagh's theory.
[Cauchy puts o.'^ + 6^ = —k"^. We shall consider the consequences
of this shortly.]
Hence (36) becomes
D*  D'*i = ^(/i  n') — ' . , \ ' (o8)
c^ l ^ I
Cask I. n = n' (Green).
Then
WJi tan (<p  <!>') f 1 + M' tan" (<p + <!>') ) * .gg.
tan (<!> + (l>')\l + M2 tan* (f  ff,')) ' ' ^ ■>
W and R being the amplitudes of the reflected and refracted waves, and
2 "I
M eaual to ^ , while the diSerence of phase between the incident
^ 1^^ + 1
and refracted waves is e where
cot e = L cot (<}> (p>) . . . . (40)
while between the reflected and refracted waves it is e', where
cot e' = ^ cot (r/, +i>') . . . . (41)
Case II. D = D' (MacCullagh's corrected theory).
The equations are very complicated and lead, when the difference in
the rigidities is very small, to two polarising angles of 22^° and Q'7^°
respectively, results which are thus utterly at variance with experiments.
Cauchy's theory leads to results the same in form as Green's, if we
substitute — £ sin for M, e being a certain small constant.
The solution is contained in the above equations if we tabe
a'2 + b^=  l\ a,'2 + b'= t,^
ON OPTICAL THEORIES. 191
and put
27r/l 1 N
T{kkJ = ' • ■ . . (42)
In Eisenlohr's account of Cauchy's work it is assumed at first that
the normal waves travel with the same velocity as the transverse, and
then the solution is modified by putting for X^^, \", the wave lengths of the
normal waves, the values — l,,l/ — 1 and — Z'V — 1. This modifies
tpii and ^", the angles of refraction and reflexion of the normal waves, so
that their sines become imaginary, while cos ^^^ is real and negative,
cos 0" real and positive.
A difierence of phase is thus produced, determined by the following
•equations : —
tan e = p tan (^ — 0'),
where
and
tan e'=^ tan (^ + f'),
V =
m."viii — l'
Jamin's results show that^ is very small ; hence we may write
where u is small, and then
2m sin (f>
^ ~ tVTt^ + sin^ 0) • • • . (43)
Cauchy puts p = e sin f, when e is a small constant. Hence we must
suppose that t is great compared with f.
Lorenz and Lord Rayleigh have both pointed out the serious obiec
}^^ *'° «*" "'^'^^ *° ^^^ *^®°^y ^° *^^s fo^"^ The equation to determine * is
d^ df '^W medium will be essentially unstable.
Moreover, if Z; be a constant, e varies inversely as X, and chromatic effects
, near the polarising angle should be much more marked than they are
I 1 have, however, given an account of Eisenlohr's paper mainly because
ot another suggestion he makes, which renders it very nearly identical
with Green s. He suggests that the normal or preesural waves mav
' vanish by a sort of total reflexion, their velocity being very great com
, pared with that of the transverse waves.' So that we have X , and X"
very large instead of imaginary, and from this he finds
_ \,^  X"^
^ X ^ + \"2 ("^^
This vanishing by a sort of total reflexion is exactly Green's theory, for
192 REPORT — 1885.
if x' be the angle of refraction for a normal wave produced by a trans
verse wave incident at an angle <j>, then, with the notation of Lord Ray
leigh's paper, 71 sin^ x = ™ sin^ ^, and hence x is iniaginary unless (p is
less than sin"'(n/?u). That is to say, if wt be infinitely large, the effects
of the pressural wave are entirely confined to the surface, and, indeed,
for this total reflexion, if we may so call it, of the pressural wave to
take place, it is practically not necessary for the ratio of n to m to b©
zero. If, for example, n/iu = 1/100, there will be total reflexion if f is
greater than 0° 85', and for so small an angle of incidence as this the
component of the vibration normal to the surface on which the pressural
wave depends would be too small to produce a measurable efiect on the
transmitted light.
If we put \^JX" = f.iQ, then jJq is the refractive index of the medium
for the normal vibrations, and we have for ^j
p':^^ (^5>
Ho
' + 1
Now, it was shown, first by Haughton,' and then by Kurz, that the
expressions (3941) agree with experiment very closely if M or p be
treated as a constant to be determined by experiment, and if we suppose
p to have the form just given, then for sulphuret of arsenic, for which
fi = 2454, according to Jamin, ^Iq = TOSS. Green, going further into the
mechanism of the motion, has shown, however, that on a strict elastic
sohd theory we must have \,J\" = \/\' and fJo^h' The last conclusion
Eisenlohr calls ' durchaus unhaltbar,' and in this he is right if he means,
that it does not agree with experiment, but wrong if he means that there
is a flaw in Green's theory. The suggestion that ^ and /iq may be
diff'erent is due to Haughton,^ but the reasons he has assigned for it have
been shown by Eisenlohr to be invalid. Lord Rayleigh has suggested
others which have great weight, and the importance of which will be
more clearly seen when we come to consider some recent theories based
on the mutual reaction between matter and the ether. The large quan
tities m and m' are, in Lord Rayleigh's paper, eliminated from the equa
tions by means of the relations
viia'^ + h"") =Dc2,
D and D' being the densities of the ether in the two media.
Now, in the pressural wave we are only concerned with a layer of
ether close to the bounding surface, and Lord Rayleigh's suggestion is
that, although the transverse vibrations are affected nearly in the same
way as if the transition were instantaneous, it may not be so for the
surface waves, and that therefore we may put D/D' =yuo^ where /uq is less
than fj. There are, I think, even stronger reasons for supposing /.iq and
^ to be difierent to be derived from the theory I have already referred
to, which will be developed later.
Thus the papers of Lord Rayleigh, Lorenz, and Eisenlohr show, con
clusively, that Neumann and MacCullagh's theory is inadmissible, and
that Green's strict elastic solid theory, when slightly modified in a per
' Haughton, Phil. 3/aff. (S. 4), vol. vi. p. 81 ; Kurz, Pog/;. Ann. t. cviii.
2 Haughton, Phil. Mag. (S. 4), vol.vi. p. 81 ; Eisenlohr, Pugg. Ann. t. civ p. 3t6.
ON OPTICAL THEOEIES. 193
fecfcly reasonable way, leads to results agreeing very closely with experi
ment, while Canchy's method of treating the pressural wave requires
an unstable condition in the ether.
In another paper Lord Rayleigh ^ considers the problem of reflexion at
the confines of a medium of variable density. The incidence is supposed
to be normal, and in, the particular problem solved completely, the density
is supposed to vary as the inverse square of the distance from a fixed plane
parallel to the surface. This variable medium extends between the two
planes x = x^^, a; = a'2, and the density is constant on the other sides of
these planes, and it is shown that if the thickness of the variable layer is
not very different from the difference in the wave lengths in the two, then,
for the case in which the two media are air and glass, the reflexion will
be excessively small.
§ 5. The paper by KirchhoS" in which the problem of reflexion and
refraction is considered has been already referred to. The theory there
given is, in its results, nearly the same as those of Neumann and
MacCullagh.
The ether is not treated strictly as incompressible, though it is
supposed that only transverse waves are propagated, and therefore that
the equation
du dv dw /N
dx d)j dz
is satisfied without the coefficient A becoming very large. These trans
verse waves falling on the interface of the two media would tend to set
up longitudinal vibiations. Some surface action, however, is supposed to
go on over the interface, the result of which is to quench these vibrations
and the condition that this surface action should involve neither loss nor
gain if energy is formed. This, with the three equations implied in the
continuity of the displacement, makes four conditions from which the
intensities and planes of polarisation of the reflected and refracted waves
can be found.
The theory differs from MacCullagh's merely in recognising the
possibility of the existence of the normal waves, and then accounting for
their absence by means of some unknown surface action. It is not a strict
elastic solid theory, nor does it attempt to explain of what nature the
surface forces are which quench the normal waves. The formulas to
which it leads are identical with MacCullagh's,' and do not offer any
explanation of the change of phase observed by Jamin. It can hardly
be looked upon, therefore, as a satisfactory explanation of the phenomena,
nor can we regard Kirchhoff's principle, as the fundamental hypothesis
is called by various German'* writers, as one which may replace the true
surfece conditions of an elastic solid.
Chapter V. — Metallic Reflexion.
§ 1. Various experimenters — and among them Brewster, MacCullagh,
Briot, Airy, Neumann, De Senarmont, Jamin, Quincke, Wernicke, and
Conroy — have investigated the optical efl'ects produced by metallic re
' Lord Eayleigh, Proceedings of London Math. Soc. vol. xi. No. 159.
' Kirchhoff, Aih. der Konigl. Akad. zu Berlin, 1876
' See Glazebrook, ' On the Keflexion and Refraction of Light,' Proc. Camh. Phil
Soc. vol. iii. p. ,329.
* See Ketteler, Voigt, etc.
1885. o
194 KEPORX— 1885.
flexions. They have shown that, in general, plane polarised light becomes
elliptically polarised by such reflexion, and have measured the difference
in phase between the components polarised in and perpendicular to the
plane of incidence and the ratio of the intensities of these two vibrations.
MacCullagh ' was the first to attempt to express the laws of this
elliptic polarisation mathematically. He supposes that in the case in
question the angle of refraction becomes imaginary, so that we have
sin
, , sin / , . . \
in rf)':= Ll cos Y + i sm X ),
m \ J
J, cos 0/ / , ■ • /\
cos d)'= ;i( cosv' + ismx ).
He then substitutes these expressions in the values given by Fresnel's
theory for the amplitude of the reflected ray, which he shews may be
written in the form a+fe v' — i.
Thus the intensity of this ray will be represented by a^ + V', and the
difference of phase between the incident and reflected rays will depend on
tan ~^b/a ; a and b are functions of w, in', x, and x', and these quantities
are connected by the equation sin'^^' + 008^^0' ^1, which leads to two con
ditions, giving m' and x' in terms of vi and x
The final formulae are : —
(1) Light polarised in the plane of incidence.
p = D' + cos''  2D cos <p cos (xxO (4,q)
D^ + cos'^ + 2D cos cos (x— x')
t^n24=^^^^^^^pO. . . . (47)
X COS'' (j)—D^
(2) Light polarised perpendicular to the plane of incidence.
T/2 _ ''"'* cos'' + D^ — 2Dm^ cos cos (y + xQ fAQ\
7n* cos^ <p + D"^ + 2D»i2 cos f cos (x + x')
tan2/ = ^P^\""^t'^"^^t^^^ . . (49)
Where D'* = m'' + sin"* — 2m^ sin* f cos 2x
and D'' sin 2 (x— x') = '"^^ ^™ ^X
} • . (50)
These formute are simplified in the case of metals from the considera
tion of the fact that the proportion of light reflected at normal incidence
is nearly unity. It follows from this that m is very large and x' very
small, so that we may put sin x' = 0, cos x' = 1 i^ ^^^c equations, and
hence m' = cos /cos 0',
And for Case I. —
jj m' + m'"^ — 2mm' cos x ^
m"^ + m'"^ + 2invm' cos x
, 2:rS 2inm' sin x
\ m'^ — m^ )
(51)
' MacCullagh, Pruc. Irish Acad. vol. i. pp. 2, 159 ; vol. ii. 376 ; Trans. Irish Acad.
1 xxviii. Pt. I.
ON OPTICAL THEORIES. 195
and Case II. —
j,2 1 + TO^W'* — 2«lMi.' COS X
1 + m?rnl^ + 2min' cos v
., o , • \ ■ ■ (52)
, ct o' zmm sin v
tan 2;r  =  ^
§ 2. Cauchy ' has also given equations founded on his principle of con
tinuity and the assumption of a peculiar form for the refracted ray which
agree closely with those just established. His complete theory was never
published by himself, and was first given by Eisenlohr. It has been
further developed and criticised in some important points by Lord
Bayleigh. Eisenlohr ^ takes for the displacement in a metal at a dis
— (p— ;•)
tance r from a source of light the expression e ^' ' where X' is a com
plex quantity connected with A, the wave length in air, by the equation
X = X' Re'«.
Hence, using d and 8' to denote the angles of incidence and refraction,
we have
sin = Re'"^ sin 6' . . . . (53)
The surface conditions of the continuity of the displacement and of
the stresses become, as v^e have seen, identical with Cauchy's conditions
of continuity of motion in the case in which the rigidity of the ether is
the same in the two media, and the expressions for the intensity and
change of phase for light polarised in the plane of incidence are most
«asily obtained by transforming Fresnel's sine formula, which is strictly
true.
To effect the transformation put
c»
cos
2u
=
1
cos 2a sin^
d\
C2
sin
2u
___
sin
2a sin2 d
(93)
m a
IP
Then the intensity in the reflected wave is
P = tan (/•  ^tt) .... (54)
where
cot/= cos (m + a) sin 2tanip— V
while d, the change of phace, is given by
tan d = sin (a + u) tan 2tani f^°lf\ ^ ^ (55)
These values agree with those given by MacCullagh if we put
R = m, a=  X,
' Cauchy, C. B. t. ii. p. 427 ; t. yiii. pp. 553, 658 ; t. ix. p. 727 ; t. xxvi. p. 86.
Ziouville's JomttmI, t. vii. p. 338.
* Eisenlohr, Poffj. Ann. t. civ. p. 368.
02
196 EEPOET — 1885.
and therefore c sec = m', u = x' \ C56>
For Hglit polarised at right angles to the plane of incidence, Eisenlohr
proceeds by transforming Fresnel's tangent formula in a similar manner,
and finds , „ ^
I'2 = tan (gi^) ' • • • (57)
where
cot g = cos (a — u) sin 2tan' ( ^ J . . (58)
and the change of phase is given by
tan d' = sin (a — u) tan 2tan"'— — '■ — , . . (59)
^ ' K. cos
Hence in the general case the ratio of the amplitudes of the two
reflected components is tan /3 where
cos 2/3 = cos (a + «) sin 2tanM ^— — ^ J . . (60)
and the difference of phase is given by
tan (d'  d) = sin (a + u) tan 2tan' ^_^_— ^ j .
(61)
These last equations depend on Fresnel's tangent formula, and this
we know is not strictly true for transparent bodies. It is hardly
probable, therefore, that the final equations for the difference of phase
and the ratio of the amplitudes can be accepted as representing accurately
the phenomena, and, in fact, Cauchy's theory as here developed isno great
advance on MacCuUagh's original expressions, with which it agrees
throughout.
In this theory the expression for the disturbance in the metal
IS e
Ae i ''^'""^ sin — (rR cos a  ct).
k
Hence the velocity of wave propagation is c/R cos a, as against c in
air, and R cos a may be called the refractive index of the metal, while
R sin a measures the coefiicient of absorption. Now Jamin, Quincke,
and others have measured the quantities d — d' and /3 of the formulas
above, and from these Eisenlohr, in the paper already quoted, has calculated
the values of R and o. He finds that for silver a = 83°. This result Lord
Rayleigh has made the basis of a serious criticism on the whole theory.
Lord Rayleigh ' endeavours to attach a physical meaning to the con
stants in these formula?, and in so doing starts from equations taken to
represent the motion in the medium.
Thus, for light polarised in the plane of incidence he assumes
' dt^ dt Vdx* di/J
' Hon. J. W. Strutt, ' On the Reflexion and Refraction of Light by intcnbel3r
Opaque Matter,' PMl. Mag. May, 3 872.
ON OPTICAL THEORIES. 197
with the solutions for the two media,
/ _ ^'g i(ax+b)j+vt) a. ^"e i(ax+by+vl).
(63)
^ __ ^ g i{a,x+bij+vl)\ J ^ '
where
a = — ^ cos 0, 6 =— sin e, ^; = — — ,
\ A. A
being the angle of incidence. If we put y^ = n/D, y^i = n/D,, we get
from the differential equations —
<±i;=.y'rii^)=,\s^j. . . (64)
a2 ^ j2 ^^2 y^ D^^y
From this we get sin 6' =  sin 9, and hence /x is the quantity which
F
we have denoted by Re'".
Hence We'^^ = '^~Jl  i^). . . (65)
yi^\ D^vJ
Thus R2 cos 2a is positive, and R^ sin 2a is negative, so that 2a lies
between and — ^tt and tan 2a = hlB^v. Again, in the expression for
the refracted wave we have a^ = [ja when 6 is zero, and hence we find
that the real part of /i is positive, the imaginary part negative, so that
finally a lies between and — ^tt. This result is contradicted by Eisen
lohr's value for silver, in accordance with which a = 83°, from which it
follows that the real part of /x^ is negative, and this Lord Rayleigh says
is tantamount to assuming the medium to be unstable. Eisenlohr ' has
repHed to this that the objection is really one to the form of equation
assumed by Lord Rayleigh, and that according to other theories (e.ij.
Helmholtz on anomalous dispersion 2) real negative values of /x^ are con
templated. With this reply we may in a sense agree. Loi'd Rayleigh'a
objection is a valid one, however, against the supposition that the
peculiar effects of metallic reflexion may be explained by the introduction
of terms such as in the differential equations of an elastic solid
ether, and forms an insuperable argument against the attempt to account
for the effects on a purely elastic solid theory. When, however, we come
to consider the theories depending on the mutual reaction of the ether
and maiiter, we shall see that under certain circumstances the relation
between the periods of the ether and matter molecules may be such as to
give a negative value to fi^, and thus render possible Eisenlohr's value
for a.
The general value for a^ for any angle of incidence caay be shown to
be given by
«! = "^Rc < cos (u + a) + L sin (« + a) > . . (66)
< ' Eisenlohr, ' On the Keflexion of Light from Metals,' Wi^d. Ann. t. i.
2 See p. 220.
198 EEPORT — 1885.
c and ?( being defined by the equations of page 195, so that tbe expres
sion for the refracted wave is
^^g?^pRcsm(« + a) sin— JRracos (u + a) + ysind + Yt\,
where, it must be remembered, x is measured in the negative direction.
Thus the coefficient of absorption is
— Resin (u + a).
According to the experiments of Jamin and Quincke, the refractive index:
R cos a for metal varies between ^ and i.
§ 3. Wernicke,' however, deduced, from some experiments of his own,
values lying between 3 and 4. Wernicke's experiments, however, were
made by measuring the light transmitted at various angles of incidence
by thin films of metal, and assuming that the light absorbed by a thick
ness d may be expressed by fc/i''"^'^^', while the refractive index ft is given
by sinf^/sinfl'. Eisenlohr, in the paper already quoted, shows that the
quantity calculated by Wernicke is really {R^ + sin^y}^, and that his
experiments confirm Jamin's and Quincke's.
In the second paper quoted Wernicke suggests, as the complete equa
tions of motion, the form
.+Zh^ = (AB)f + Bs^''^ + Zk't(v''^) . . (67}
dt'" \ Jdx dtf^y J
and other equations might be suggested which would give for the dis
turbance in the metal due to a point source expressions of the form
t._27r
A£~^''sin
fbr — vt\
Chapter VI. — Diffeaction and the Scatteking of Light by Small
Particles.
§ 1. The principle first enunciated by Huygens, and applied so trium
phantly by Fresnel to the phenomena of diffraction, which consists in
breaking up a wave front into elementary portions, calculating the effect
of each in disturbing a distant point, and then finding the total dis
turbance at that point by simply summing the effects due to each ele
ment of the wave front, is a direct consequence of the fact that the
disturbances and velocities are so small that their squares and higher
powers may be neglected. The differential equations found for the
motion are linear, and the complete solution is the simple sum of all the
individual solutions. Again, it is fairly clear that the disturbance pro
duced at any point by an element of a wave front will vary as the area of
the element and the reciprocal of the distance between it and the point
answered ; but it is not so clear how the effect is related to the angles
which the line joining the element and the point make with the wave
normal and the direction of vibration respectively.
In Fresnel's theory of diffraction the consideration of effects produced
• Wernicke, ' On the Keflexion of Light from Metals,' Pogg.Ann. t. clix. and clx.
ON OPTICAL THEORIES.
199
by tlie vaxiation of these angles is omitted, and that, too, with perfect
justice, for lie is only concerned with the effects in the neighbourhood of
the normal to the primary wave, and the dimensions of the diffracting
aperture ai'e small compared with the distance between it and the point
at which the effects are considered, so that the change in either of these
angles over the whole area of the diffracting area is small.
Again, it is clear that the effect will be a circular function of r—vt, r
being the distance between the element and the point at which the dis
turbance is sought, and v the velocity of propagation ; but the simple
theory does not indicate the relation between the phase of this circular
function and that of the function representing the disturbance in the
original wave.
§ 2. Both these questions received their complete and final answer in
the year 1849 from Professor Stokes.' We will quote a few words from the
introduction to his paper : ' TJ^e object of the first part of the following
paper is to determine on purely dynamical principles the law of disturb
ance in a secondary wave, and that not merely in the neighbourhood of
the normal to the primary wave, but in all directions. The occurrence of
the reciprocal of the radius in the coefficient, the acceleration of a
quarter of an undulation in the phase, and the absolute value of the
coefficient in the neighbourhood of the normal will thus appear as parti
cular results of the general problem.'
The equations assumed for the motion. are those of an elastic solid in
the form given by Green —
Jdx
etc., where
dx dy dz
(68)
In the preliminary analysis the important general theorem involved in
the equations
is proved.
It is then shown that the solution may be written
S = ?i 4 £2
where
and
^ _ '^ = etc
ay ax
dx dy dz
d^ _dj]2
dy dx
dx dy dz
'Stokes, 'On the Dynamical Theory of Diffraction,' Trans. Camb. Phil.
vol. ix. p. 1 ; Math, and Phys. Papers, vol. ii. p. 243.
(70)
(71)
(72)
Soc.
200
EEPOKT — 1885.
and that hence
^'="Mlr~^'°'^"^'^'^4l[,
1 (yw'"  z^")dv
(73)
It is proved that ? and w', at", w'" satisfy the equation
— . = a^ V ''t
d iO 7 9 _, 9
dt^
(74)
. (75)
and hence, hy Poisson's solution,
where /and F are the initial values of I and dljdt respectively.
If, then, the values of o and dljdt, w and dujjdt be given initially
everywhere, the last equation, with the similar one for w, enable us to find
S and w at any moment throughout the space considered, and then the
equation (73) give us ^, ??, and C
In solving the equations for c, w, it is clear that if we first find the
part of the solution due to the initial velocity, the part due to the initial
displacement may be obtained by substituting in the solution for the
initial velocity the initial displacement, and then differentiating with
regard to the time ; and this proposition is proved generally for a system
in which the forces depend only on the configuration of the system, and
which is executing small vibrations about an equilibrium position.
The integrals are then modified by suitable transformations.
For
L we have £,= —, where ii'=
dx 47r
dv.
Thus — 4<Tr\h is the potential of matter distributed throughout space
with density S, and finally it is shown that
^ =
f
47r
(uqX + VqIj + Wqz) ~ (raf)
. (76)
where Uq, Vq, Wq ^^e the initial values of the velocities at the point x', y', z',
at which dv is an element of volume, r the distance between x', y', z'
and X, y, z, the point at which ^ is to be found. From this ^i can be found,
and in a similar manner So The terms
ir
Vu
<^[ arise from a wave of
dilatation which is in general set up by any arbitrary displacement, and
which travels through the medium with velocity a. If the initial disturb
ance be such that Cq = dcQJdt = everywhere, then this wave will not be
formed.
The terms
''2) Vij
^2 arise from a wave of distortion which ti'averses
the medium with velocity h. If a disturbance be produced at a point O,
and last there for a time r, then the motion at a point P, at a distance r
from 0, will not commence until after an interval t, where t = r/a, P will
be disturbed by a wave of dilatation lasting for an interval r ; it will be
disturbed by the wave of distortion after a time rjh, and this disturbance
will last for an interval t.
ON OPTICAL THEORIES. 201
The general integral is then applied to two cases, which must be care
fully distinguished from each other. In the first case, suppose that a
periodic force acting parallel to a fixed direction acts throughout a given
element of volume in the medium. Let the plane of xz contain the fixed
direction, and let the axis of a; make an angle a with it. Let D be the
density, and T the volume of the element, and let (DT)\/'(Orf^ be the
velocity communicated to it in time dt.
Then
r
cos n ,( r \ . cos a fi^
47rD
=
sin a .f , r \ sin a f*
^=4
(77)
Now, we have seen that in the ether the ratio ajb is probably very large,
hence the first term in £, on which the normal vibrations depend, is pro
bably very small compared with the first term in C The molecules of
an incandescent body may be looked upon, at least very approximately,
as centres of disturbing forces, and the above equations show us how it
is that from such centres transverse vibrations only are propagated.
If the ether be absolutely incompressible, so that a/b is infinite, then
longitudinal vibration would be impossible.
Suppose, now, the first term in 4 omitted, and pnt/(i) = c sin 27rit/X,
Then for the most important term we have —
y c sin a . 2
"(fc^r) . . . (78)
and the first term in I is of the order Xjirr compared with the leading
term in i^. Hence, except at distances from the source which are com
parable with the wave length, the terms in I may be neglected, and the
motion is strictly transverse.
This solution applies to the case of an element of volume vibrating in
any given manner and emitting light into the surrounding space. Every
thing is symmetrical around the direction of vibration of the element of
volume. It does not apply, as has been supposed by some writers, to
the problem of diffraction ; for in this case we have a train of waves being
propagated through an aperture, and producing disturbance in the medium
beyond.
Let us suppose the aperture to be plane, and that plane waves are
bemg propagated through it in the direction of its normal; take
this for the axis of x, the plane of the aperture being x = 0, and the
axis of z the direction of vibration. Let Oj be a point in the aperture,
and consider the disturbance propagated in a small interval of time r,
across an element c^S, at Oi. This disturbance occupies a film of thick
ness It, and consists of a displacement f{ht') and a velocity hf'{ht').
Thus, for a point O, at a distance r from O^, and at a time t, given by
i = t' + r/h, the initial disturbance is the above displacement and velocity
extending over a volume brdS about ; and if I, m, n are the direction
202
REPORT 1885.
cosines of Oi 0, measured from Oj, then the values of I, rj, Z depending on the
initial velocity are —
mnds
(79)
while the values depending on the initial displacement are
Pnds
i" = 
1," = 
r = KI
47rr
Imnds
ffitA '
(80)
From this it follows that the vibration at O, arising from that at 0,,
lies in the plane through OiO and the axis of z, and is perpendicular to
the radius OjO ; and if (j> be the angle between the axis of z and the line
OiO, that between OiO and the wave normal, the value of this dis
placement is —
' ^ . . (81)
!: = ^ fl + cos o") sin ff fuA
Hence if
f(bt) = c sin — bt,
^ = f^/'l + cos e\ sin f cos — fbtA . . (82)
and the total efEecfc at will be found by integrating this over the whole
wave front.
We have thus found the complete expression for the law of disturb
ance in the secondary wave, and can see in what way it involves and (ji,
and how its phase is related to that of the disturbance over the primary
wave.
The theory of diffraction given by Fresnel, and applied by him to
points in the neighbourhood of the principal wave normal, is thus fully
justified, since for such points 6 is small, and cos d therefore approxi
mately unity, while ^ is nearly constant. The expression shows that an
addition of a quarter period must be made to the phase ; but this will not
affect the form of the diffraction pattern obtained.
But the results of the investigation are of even more importance in
their bearing on the relation between the position of the plane of polari
sation and the direction of vibration of plane polarised light. For con
sider a ray diffracted in a direction making an angle d with the incident
wave normal, and let the plane containing the incident and diffracted
ray be called the plane of diffraction, and let the directions of vibration
ON OPTICAL THEORIES. 203
in the incident and diffracted rays make angles a,, a,; with the normal to
the plane of diffraction. Then the diffracted ray and the two directions
of vibrations lie in the same plane, and the directions of vibrations are
normal to the respective rays. Thus, if we form a spherical triangle by
drawing lines from the centre of a sphere, paiallel to the normal to the
plane of diffraction and to the two directions of vibrations, since the
direction of vibration in the diffracted wave is the projection on that
wave of the direction of vibration in the incident wave, we have
cos d = tan ftj cot a^ . . . . (83)'
Now, let cr and a be the azimuths of the planes of polarisation of the
incident and diffracted Hght, measured from a plane normal to the plane
of diffraction. Then, on Fresnel's assumption that the direction of vibra
tion is normal to the plane of polarisation, we have
•=^ = 2 " "=2+""^'
and tan a = sec 6 tan w ;
while on MacCuUagh's hypothesis
'B7 = a,, a = uj,
and
tan a = cos 6 tan to ... . (84)
These two formulae can be tested by experiment, and afford a means,
therefore, of deciding between the two theories of reflexion, and of deter
mining the question whether reflexion be due to a change of density or
to a change of rigidity in the ether ; for the values of a corresponding to a
series of values of ro can be observed for any given angle of difiraction,
and if the values of w be taken at equidistant intervals, the values of a,
and therefore the positions of the plane of polarisation of the diffracted
light, will not be equidistant, but will on the first hypothesis be crowded
towards the plane of diffraction, while on the second they will be crowded
away from that plane.
Professor Stokes was the first to carry out a series of observations of
this nature ; he employed a grating ruled on glass at the rate of 1,300
lines to the inch, and the results of his experiments are decisive in favour
of Fresnel's hypothesis. The experiments are troublesome, and the com
parison of the results with theory is complicated by the fact that the
refraction through the glass plate on which the grating is ruled also
produces a change in the position of the plane of polarisation. The
amount of this change is the same on the two theories, and tends to
produce a crowding of the planes of polarisation away from the plane of
diffraction, an effect opposite to that produced by diffraction on Fresnel's
theory. Moreover, we may suppose that, when the ruled face of the grating^
is towards the incident light, either the diffraction takes place in air so
that the wave enters the glass obliquely, or that the diffraction takes
place in the glass after the light has entered the first surface normally,
while when the ruled surface is away from the incident light the diffrac
tion may take place in air after passing normally through the glass, or in
the glass so that the light after passing normally through the first sur
face emerges obliquely.
'204 EEPOET — 1885.
In any case we shall have
tan a = m tan •ar , . . . . (85)
where in is a function of the angle of diffraction and the refractive index,
which can be calculated on either of the above hypotheses.
The results were reduced by plotting from the experiments a curve
with log m as ordinates and 0, the angle of diffraction, as abscissae. The
curves given by the two theories on either of the above assumptions
as to the relation between diffraction and refraction were also drawn, and
a comparison of the two results ' leaves no reasonable doubt that the
experiments are decisive in favour of Fresnel's hypothesis, if the theory be
considered as well founded.' And, moreover, the comparison shows us
that we must suppose the diffraction to take place before the refraction.
Thus, when the grooved face is towards the incident light we must sup
pose the wave to be broken up in the air and then to be obliquely
refracted through the glass, while when the grooved face is away from
the light the wave must be treated as if it were diffracted in the glass
and then obliquely refracted out, and Professor Stokes shows that it is
a friori more probable from physical reasons that this is what takes
place.
§ 3. In the results of the experiments a certain amount of irregularity
is pi'oduced by the want of symmetry of the grooves of the grating, and
Holtzmann,' who in 1856 repeated Stokes's experiments, failed to obtain
consistent results with glass gratings, and had recourse in consequence to
a Schwerd's lampblack grating ; with this he obtained results more in
accordance with the theory of Neumann and MacCullagh than with that
of Fresnel.
Holtzmann thought that Stokes had neglected to consider the effect of
the longitudinal waves, ' and to this neglect he attributes the error of
Mr. Stokes ; ' and Eisenlohr,^ who * had not read the great paper of
Prof. Stokes,' attributes to him the same neglect, and endeavours to
give a theoretical account of the question from Cauchy's standpoint.
Of course both these authors were quite wrong in their estimate of
Stokes's work, and Lorenz ^ showed, from some decisive experiments of his
own, that Holtzmann's results were due to an error of his method. Lorenz
gave a fresh demonstration of Stokes's theorem, and arrived at the same
results. Lorenz appears to consider his method as more general than
that of Stokes, but this is due to a misconception on his part. The
results of his experiments agree with Fresnel's theory.
§ 4. The matter has since been experimentally investigated by
Quincke,'* who showed that the method of forming the grooves on the
grating was of the utmost importance, and whose experiments led to no
decisive results, and moi"e recently by Frohlich.* Frohlich investigated
the polarisation of the light reflected from a glass grating, but did not
compare his results with theory. A few experiments of the same kind
were made by Stokes in 1852, but he also omitted the comparison with
theory.
' Holtzmann, Pogg. An?i. t. xcix. p. 446.
2 Eisenlohr, Pogg. Ann. t. civ. p. 3.S7.
' L. Lorenz, Pogg. Ann. t. cxi. p. 315.
■• Quincke, ' Experimentelle optische Untersuchungen,' Pogg. Anii. t. cxlix. p. 73.
* Frohlich, Wiedemann, t. i.
ON OPTICAL THEORIES. 205
Rethy ' developed a theory whicli covers Frohlich's experiments, and
arrived at a formula with which they agree closely, but his fundamental
principles are at fault.
In his solution Rethy adopts a method given by Kirchhoff to find the
effects of a given source of light.
The equations to be solved are, if we neglect the terms involving
dilatation,
etc., with the condition
Take
^^=v^vV
du dv diu
dx dy dz
«& = ^ sm 27r I   vj, + 2 I . . . (86)
Then $ and its differential coeliicients satisfy the equations of motion,,
and we require to find such solutions as will satisfy the equation of
continuity.
Rethy takes as solutions —
da>
• . (87)
I.
and
d<t> d<t>
'' = dy' ''=dx' ^ = ^ • •
II.
u =
rf2<& d^^ d2$ tZ^d.
~ dxdy' " —~ dydz' "^ — dx" '^ ly"^
. (88)
The distance r, of course, is measured from a point on the grating to
the point at which the motion is being considered.
Now each of these expressions of course represents the solution due
to some arbitrary motion set up somehow over the grating. In Case I.
the motion is a periodic twist of each element about the axis of 2, while
in Case II. it is an oscillation parallel to that axis. But Rethy does not
show how this motion is to be set up, nor whether it can represent the
effect of a train of plane waves falhng on the grating and there diffracted ;
and a little consideration shows that it cannot, for, according to the
ordinary assumed properties of the ether, we cannot get the wave of
twist only without linear displacement ; the second solution corresponds
to that due to the action of a periodic force at the origin generatino a
certain amount of momentum, and not to the complete effect of a train
of waves. If we compare it with Stokes's solution, we see that it is that
part which arises from the effects of the velocity propagated across the
element, and omits the part due to the displacement. Stokes's solution
applies to the case in which energy is being propagated by waves passing
across the orifice into the medium beyond, and depends on the direction of
motion of these main waves. Rethy's solutio4i is that which arises from
a centre of vibration situated on the surface, kept in motion by some
exteinal force and sending out waves in all directions into the medium.
Still, we can arrive at a formula of the same nature as that given by
Rethy, and which does agree with Frohlich's experiments, by means of a
simple extension of Stokes's principles. This consists in supposing that
' ESthy, Wied. Ann. t. xi. p. 504.
206 REPOBT — 1885.
the incident waves set np vibrations over the surface parallel to a fixed
direction, and that these vibrations lie in the same plane as the incident
vibrations, while these vibrations set up others in the diifracted waves
which lie in the same plane as those over the surface, and are everywhere
normal to the diffracted rays. Then, if eo be the angle between the
incident wave normal and the distui'bance over the surface, ^o a^id the
azimuths of the planes of polarisation on Fresnel's hypothesis measured
from the plane of incidence in the incident and diffracted waves, and c
the angle of diffraction, it can be shown that '
cos <po tan f = sin 2 cot Cq + cos S sin (po . . (89)
This expression is given by Rethy, and agrees closely with the results
of Frohlich's experiments which were made with two gratings — the one
of 19' 76 lines to a millimetre, the other of 162 lines to a millimetre.
The value of eo depends on the angle of incidence when this vanishes,
so that the vibrations in the incident wave are parallel to the surface
. Sq — 90°, and the above formula becomes identical with Stokes's.
In comparing the two it must be remembered that the azimuths of
the planes of polarisation are measured, in Stokes's expression, from the
normal to the plane of incidence, while in Rethy 's they are measured
from the plane of incidence.
A careful series of experiments by Cornu'^ also lead to the conclusion
that the vibrations are normal to the plane of polarisation. This con
■ elusion coincides with that arrived at by Lord Rayleigh and Lorenz from
considerations based on the phenomena of reflexion and refraction, and
is further strengthened by the phenomena of polarisation produced when
light is scattered by a series of small particles.
§ 5. Before considering this, reference must be made to a paper by
Professor Rowland,^ of Baltimore, on the subject. This paper will be
more completely discussed when we come to the electromagnetic theory,
to which it more properly belongs. Professor Rowland, however, con
siders that he has discovered an error in Stokes's work, in that according
to it ' when a wave is broken up at an orifice the rotation is left discon
tinuous by Stokes's solution.' It is not quite clear, however, how this
criticism is intended to apply ; for the rotation in the main wave is
completely determined when the displacement is known. Now, Professor
Stokes has shown that when the orifice is of finite size the aggiegate
disturbance at any point due to all the elements of the orifice, as found by
his formula, is the same as if the wave had not been broken up. The
rotation, therefore, as given by this formula is also the same.
Again, the rotation is propagated according to the same laws as the
transverse disturbance, and hence the elementary rotation due to a given
element of a wave propagated in a given direction is related to the
direction and to the total rotation of the element in the same way as the
elementary displacement propagated in that direction is related to the
Actual displacement.
Thus, if the displacements over the wave be
^ = 0, r, = 0, i: = c sin^^ {ItxX
• See GlazebroQk, Proc. Camh. Phil. Soc. vol. v. p. 254. ' Cornu, C. R.
' Rowland, ' On Spherical Waves of Light,' PMl. Ma^. June, 1884.
the rotations are
ON OPTICAL THEORIES. 20^
0, — c COS ^(bt—x), 0;
A. A
and the elementary rotation to which this gives rise is
W2= — Tr <^^S (1 + ^°^ ^) s^^ 4' sin ^ (ht — r),
A / A
■>l> being the angle between the axis of y and the radius vector r. This
elementary rotation takes place about a line perpendicular to the radius
vector, and lying in a plane containing it and the axis of y.
On passing from one medium to another the rotation is not neces
sarily continuous. The only surface conditions are that the displace
ments and the stresses are the same on the two sides of the surface of
separation, and if the rigidity of the ether be diflPerent in the two media
the rotations will be different also. But Professor Stokes's solution
does not apply to this case, and for the case to which it does apply is
complete.
Chapter VII. — The ScATTERrao of Light by Small Particles.
§ 1. In his experiments on the light scattered from precipitated clouds
of fine matter, Tyndall ' showed that when the particles are sufficiently
fine the light emitted laterally is blue in colour, and in a direction per
pendicular to that of the incident beam it is completely polarised.
The full explanation of this was given by Lord Rayleigh in 1871 in a
series of papers * having an important bearing on our present subject
the relation between the plane of polarisation and the direction of vibration
of plane polarised light. Professor Stokes, in his paper on fluorescence,^
had indicated the connection between the two questions.
For consider a beam travelling horizontally, and look at it vertically
downwards: the scattered light is in great part polarised in the plane of re
flection. If the scattering particles be small compared with the wave length
of the incident light, the vibrations in an incident ray cannot be at right
angles to those in a scattered ray. For the incident vibrations are
affected by the dust particles, which in consequence of their very great
mass relative to the ether remain practically at rest.
We may treat the problem as if the dust particles moved exactly as
the ether which they replace would do, and then superpose on this motion
an equal and opposite motion. The first motion will not affect the
regular propagation of the waves. In consequence of the second the
particles become centres of disturbance, and set up other motions in the
ether. These other motions will depend on the direction of apparent
motion of the dust particles, and the optical effect in any direction will
depend on the component of the motion at right angles to that direction.
Now, the reflected ray is polarised in the plane of reflexion. If, then the
> Tyndall, Phil. May. (4). vol. xxxvli.
= J. W. Strutt, ' On the Light from the Sky, its Polarisation and Colour,' Phil
Mag. Feb. and April, 1871 ; ' On the Scattering of Light by Small Particles,' June,
1871.
» Stokes ' On the Change of Refrangibility of Light,' Phil. Trans. 1852.
208 EEPOKT — 1885.
vibrations be in the plane of polarisation they will be at right angles to
those in the incident light, while if the vibrations be at right angles to
the plane of polarisation, they will come from the component of the
original vibration, which is at right angles to that plane. If, then, on
this supposition as to the relation between plane of polarisation and
direction of vibration the incident light be polarised at right angles to the
plane of reflection — i.e., in the case before ns in a horizontal plane — the
light scattered in the vertical direction should vanish, and this is found
to be the case. This general reasoning is substantiated by Lord Ray
leigh in the papers before us by mathematical reasoning, and, moreover,
he shows that the intensity of scattered light in any direction varies
inversely as the fourth power of the wave length.
This may be seen from a consideration of the dimensions involved.
The ratio of the two amplitudes in the scattered and incident vibra
tion will be a number. It must also involve the volume of the dust
particles, being directly proportional to it, and it also will be inversely
proportional to r, the distance from the disturbance ; it must therefore
depend on T/X^r.
The mathematical expression for the disturbance is found as follows: —
Let D' be the density of the ether in the dust particles, D in the space
surrounding them. Let the vibrations in the incident wave, when they
o
strike the dust, be given by A cos — hf. Then the acceleration is
^c^^ bycos^u.
In order that the wave may pass on undisturbed through the parts where
the density is D', force would require to be applied ; the amount of the
force will be
 AiD'  B) f ^y cos ^bt
per unit volume, and hence a force
A(B' T>)(^y cos ^^bt,
conceived to act at O, the position of the particle, gives the same disturb
ance as is caused by the particle. Now, we have seen in Professor
Stokes's paper that a force F cos — bt per unit of volume produces a
displacement at any other point given by
y F sin a Stt ., , .
which is this case comes to
C = A — ^^ — — ^ sin a cos ^{ht — r) . . . (90)
where n is the angle between the radius vector r and the direction of the
force F, and the displacement takes place in the plane passing through
the directions of the force and the radius vector, and is at right angles to
the latter.
ON OPTICAL THEORIES. 209
Lord Rayleigh's paper conclades with another proof of the formala
which gives the motion due to a force acting parallel to the axis of z.
Pat for the force Ze"", then the equations of motion become, when
expressed in terms of the rotation,
Hence
dij '
(62v2+7i2)a,o = f^
dz I
]z(^) ......
(91)
47r6'^
2^
A
and the integral extends over the space T, through which the force
where h=^='l
A h'
acts
Within this space ^ri—\ is sensibly constant ; and if w be the re.
sultant rotation which will take place about an axis perpendicular to the
plane through z and the radius vector,
tlTZ sin a e'*''
w ==■ — .
Hence ^= f c.cir= 'Lf smj« cos ^(Wr) . . (92)
J 47r6''r A
In the second paper mentioned above Lord Rayleigh points out that
the cause of reflexion may be diminished rigidity rather than increased
density, and that in this case a scattered ray might be composed of
vibrations perpendicular to those of the incident ray ; he then proceeds
to_ describe experiments on the composition of the light of the sky, made
with a view of showing that it is such as would result, according to the
above formula, from light scattered by small particles. And in the third
paper he discusses the motion in an elastic solid in which the density and
rigidity vary from point to point.
The problem is solved for two media differing slightly in density and
rigidity, and it is shown that in a direction normal to the incident ray
the rotation in the scattered ray, when the incident vibrations are parallel
to z, is given by
where
J3 =
Hence, if A« and aD are both finite, the scattered light can never
vanish in a plane normal to the incident ray.
1885. ^ P
210 REPORT— 1885.
Now we know from experiment that it does vanish, and hence either
An or aD must be zero. If we put aD=0, it can be shown from the
general expression for the rotation that there are six directions along
•which the scattered ray vanishes, for the components of the rotation are
given by —
An yz
^3 =  P — 'a
r r^
. . . . (94)
'"l
=
p
An
n
,.2
=
p
An
i — .
,.2
Wj
n
,.2
Now, there is nothing in the experimental results which at all leads to
such a conclusion. If the hypothesis of a variable density be adopted,
and A n be put zero, then,
W3 =
AD y
'^'^l' D r\ (95)
aD x\
^2=P p, 
U r
and the light vanishes in one direction only, viz. that of the axis of z.
This result, of course, agrees with that of the former paper, and we must
conclude that Fresnel's explanation of the cause of reflexion is the true
one, while MacCullagh's is false, and that in plane polarised light the
vibrations are perpendicular to, not parallel to, the plane of polarisation.
The theory as left in this paper does not explain the phenomenon of the
residual blue discovered also by Tyndall, who found that at a certain
stage in the growth of the particle causing the scattering some light
is discharged by the cloud parallel to the direction of vibration of the
incident light, and that this Hght is of a very intense blue tint.
Lord Rayleigh points out that this may be due to the higher powers
of aD/D, which have been omitted, and in a more recent paper, based on
the electromagnetic theory, he develops this point more completely.'
Chapter VIII. — General Conclusions.
§ 1. Space compels us to conclude with this the general account of
recent work on optical theories based solely on the elastic solid theory.
Special problems of various kinds have received their solution, but to
these we can only allude ; indeed, for several of them the general proper
ties of wave motion with the principle of interference are all that are
required. Such, for example, are the papers by Prof. Stokes, ' On the
Theory of certain Bands seen in the Spectrum,' ^ ' On the Formation of
the Central Spot in Newton's Rings beyond the Critical Angle.' ^ — This is
shown, as was suggested by Lloyd, to be due to the surface disturbance,
which takes the place of the refracted wave when the angle of incidence
> See p. 2.53.
=" Stokes, Phil. Trans. 1848 ; 3Iath. and Phys. Pajiers, vol. ii. p. 14.
» Stokes, Caml. Phil. Trans, vol. viii. ; Math, and Phys. Papers, vol. ii. p. 66.
ON OPTICAL THEORIES. 211
•exceeds the critical angle. — 'Oa the Perfect Blackness of the Central
Spot in Newton's Rings, and on the Verification of Fresnel's Formulse for
the Intensities of the Reflected and Refracted Rays.' ' In this paper is
■given the now wellknown proof of Arago's law that light is reflected in
the same proportion at the first and second surfaces of a transparent plate.
'On the Colours of Thick Plates,' ^ and ' On the Composition and Resolu
tion of Streams of Polarised Light from diSerent sources.' ^
In his ' Investigations in Optics, with special reference to the
Spectroscope,' published in the ' Philosophical Magazine ' for 1879 and
1880, Lord Rayleigh has considered the application of the principles of
the wave theory to geometrical optics, and the construction of optical
instruments. A full account of these is given in the article ' Optics,' in
the ' Encyclopsedia Britannica.'
Professor Stokes's great paper on Fluorescence '' is chiefly experi
mental. The cause of the phenomena is assigned to the vibrations set up
by the incident light in the molecules of the fluorescent substance, which
themselves react on the ether and emit the fluorescent light. According
to Stokes the vibrations in this light are never of shorter period than
those in the incident light; and he in a general way endeavours to
account for this, and shows that if the force acting on a given matter
molecule due to a given displacement be proportional to a positive inteoral
power of the displacement other than the first, then the amplitude of°the
displacements would involve the period, and there would be a tendency
to increase the amplitudes of vibrations of lower period than that of the
incident light, and to decrease the amplitudes in the case of vibrations
■of higher period than that of the incident light. Thus, in a group of
disturbed molecules we should expect all possible periods between two,
the upper corresponding to the refrangibility of the incident light, the
lower corresponding to the natural period of the molecules. This result,
known as Stokes's law, has been the cause of much discussion. Some
physicists 5 hold that they have found fluorescent substances which con
stitute an exception to it, while others," who have carefully repeated the
•critical experiments, draw conclusions in accordance with the law ; and
the weight of the evidence is with the latter.
A general account of the principles of the elastic solid theory was
given in his lectures at Baltimore last year by Sir William Thomson.^
To these we shall return in the next section.
§ 2. In concluding this part of the report we may say, then, that
while the elastic solid theory, taken strictly, fails to represent all the facts
of experiment, we have learnt an immense amount by its development,
and have been taught where to look for modifications and improvements.
We may, I think, infer that the optical diff'erences of bodies depend
mainly on differences in the density or effective density of the ether in
those bodies, and not on diflPerences of rigidity. Fresnel's general theory
•of the cause of reflexion is thus seen to be true, and Green's theory of
' Camh. and, Buh. Math. Journal, vol. iv. ; ilatli. and Phys. Papers, vol. ii. p. 89.
^ Camh. Phil. Trans, vol. ix. a Ihld.
* Stokes, ' On the Change of Refrangibility of Light,' Phil. Trans.
' Lommel, Pofjg. Ann. t. 143, p. 1.59 ; M'ied. Ann. t. iii. viii. x. ; Lubarsch, Wied.
.Ann. t. xi.
« Hagenbach, Poyrj. Ann. ; Lamansky, Journal de Phi/siqve, t. viii. ; Wial. Ann.
t. viii. and xi.
' Thomson, Lectures on Molecular Dynamics.
P2
212 EEPOiiT— 1885.
reflexion and refraction can be made to agree with experiment by the
simple supposition that for longitudinal and transverse disturbances
respectively, the ether in a transparent body is loaded differently. This
same theory of the loading of the ether will not account for double
refraction if we assume that the vibrations are strictly in the wave front.
If, however, we admit that in a crystal the vibrations may be normal to
the ray, instead of in the wave front, Fresnel's beautiful laws follow at
once from the equations given by Lord Rayleigh, which are quite con
sistent with the theory of reflexion and refraction, but there is a diffi
culty in dealing with the pressural wave. Neither of the strict elastic
solid theories of Green can be accepted as representing the flicts of ex
periment, and the interesting modification of Green's theory suggested by
De St. Venant fails also. In all there are too many constants for the
requirements of the experimental results, and the theories do not indicate
the meaning of the arbitrary relations between these constants with
sufficient clearness and certainty.
The suggestions of Cauchy and Briot, with the elegant mathematics ot
Sarrau on the periodic distribution of the ether in a transparent body,
lead to es:pressions for the relation between the refractive index and wave
length which agree well with experiment so long as we steer clear of
substances which present the phenomena of anomalous dispersion, but
of this they give no account.
While the formulaj given by Cauchy and Eisenlohr seem to represent
the laws of metallic reflexion witli considerable exactness, the theory on
which these formulas rest, requiring as it does a negative value for the
square of the refractive index, is inconsistent with the conditions of
stability of an elastic solid.
Nor is it surprising that a simple elastic solid theory should fail.
The properties we have been considering depend on the presence of
matter, and we have to deal with two systems of mutually interpenetrating
particles. It is clearly a very rough approximation to suppose that the
eSect of the matter is merely to alter the rigidity or the density of the
ether. The motion of the ether will be disturbed by the presence of
the matter ; motion may even be set up in the matter particles. The
forces to which this gives rise may, so far as they afiect the ether, enter
its equations in such a way as to be equivalent to a change in its density
or rigidity, but they may, and probably will, in some cases do more than
this. The matter motion will depend in great measure on the ratio
which the period of the incident light bears to the free period of tbe
matter particles. If this be nearlj unity, most of the energy in the
incident vibration will be absorbed in setting the matter into motion, and
the solution will be modified accordingly.
Part III.
THEORIES BASED ON THE MUTUAL BE ACTION BETWEEN
THE ETHER AND MATTER.
Chapter I. — The Propagation of Waves through two mutually
Interpenetrating Media.
§ 1. In the optical theories hitherto considered attempts have been
made to account for the phenomena of reflexion, refiaction, and dispersiott
by the hypotheses of modifications produced in the properties of the ether
O.N OPTICAL THEORIES. 213
by the reaction of the material particles of the medium through which
the light was being propagated. According to Fresnel the density of the
ether is affected, while according to Neumann and MacCullagh it is to
•changes in the rigidity that the effects are due.
In both cases the direct effects of the communication of momentum
from the ether to the material particles of the transparent medium is not
considered. Fresnel, ' it is true, thought it ■ probable ' that the molecules
of ponderable matter should partake of the movement of the ' ether
which surrounds them on all sides,' and Cauchy,^ in one memoir, deals
with the motion of two mutually interpenetrating systems of molecules,
but without arriving at any specially important result. Voigt' states
that about 1865 F. Neumann was in the habit of treating, in his lectures,
the system of simultaneous equations relating to the motion of ether and
matter. Briot,^ in his work on dispersion, considers the direct reaction
between matter and ether particles, but in his final result equates, as we
have seen,'^ the term expressing it to zero.
§ 2. In 1867 a paper was presented to the French Academy by
M. Boussine.sq ^ on the ' Theorie nouvelle des ondes Inmineuses.' In
this paper the dynamical effects of momentum communicated by the
ether to the molecules of ponderable matter are considered as the cause
■of reflexion, refraction, polarisation, dispersion, &c.
The ether is treated as homogeneous, and of the same density and
rigidity in all bodies, and it is supposed that when light enters a trans
parent medium the molecules of that medium may be set in vibration
isochronously with those of the ether. We have thus to consider the
forces acting on such a medium, and these may be divided into three
parts: (1) those which arise from the elastic reactions of the ether,
(2) those arising from the elastic reactions of the matter, and (3) those
arising from the mutual action between matter and ether.
Now let us consider a small element of volume, containing both matter
and ether. Let m be the density of the ether, /< of the matter, u, v, to the dis
placements of the ether in the element, U, V, W those of the matter.
Then, using Green's notation, the force, measured parallel to the axis of x,
arising from (1) will be per unit of volume —
du dv dw
where 6 = , ~ + , + , .
dx dij dz
dn
For the forces arising under (2) we have to consider that injj^ acd
d^V . . .
fx j^ ^ill be quantities of the same order ; but ju is very great indeed
•compared with m, and hence U is very small compared with u. The
' ' Premier !Memoire sur la double refraction,' OSuvres completes, t. ii. p. 278.
^ Exercu'.cs d'Analjisc, t. i. p. 33.
' Wied. Ann. t. xvii. p. 473.
* Jissats sur la theorie mathcmatique de la luiuiire. Paris: 1865.
* See p. 181.
" C. R. t. Ixv. p. 235 ; Liouville's Journal, s. ii. t. xiii. p. 313. A most clear ac
count of this theory is given by M. de St. Venant in the article already quoted,
'Theorie des ondes lumineuses,' Ann. de Chim. s. ix. t. xxv. p. 368 seq.
214 EEPOKT — ]88o.
forces (2) depend on U and its differential coefficients, and it is assumed
in the theorj that in consequence of the excessive smallness of U they
may be neglected. Again, let us suppose that the dimensions of the ele
ment of volume are large compared with the distance through which the
action of an ether particle on a matter particle is appreciable. Then we
may consider the mutual reaction between matter and ether as confined
entirely to the element of volume considered, the actions taking place
across the surfaces of the element will just balance each other, and hence,,
if we consider the matter and ether as one system, the force (8) will be
zero, and the equations of motion will be
J,. + M ^ = (AB) ^_^ + B V he, etc. . . (1>
m
U is here the displacement of the matter occupying the same element of
volume as the ether, whose displacement is u, but all the displacementa
being very small, it is assumed that we may treat U and u as the dis
placements of the matter and ether, which when at rest occupy the same
element of volume. Thus XJ, V, W are functions of w, v, w and their diffe
rential coefficients with respect to x, y, z, the initial coordinates, and may
be expanded in terms of these, and it remains to find the form of the
expansion.
Conditions are, of course, imposed by the fact that the medium is
isotropic, and it is shown that so far as second differential coefficients Me
may write
U = An + C ^^^ I D v^w, etc. . . . (2)
On substituting this value of U, in the equation of motion, and assuming;
Stt / m.r + tip + pz\
H = Me ' ^ V ~ "> ) etc., we obtain
And these equations, of course, give a normal wave travelling with a
velocity [ {X + 2^1 + 4(C + D) tt^, /r^} /(p + Ap,)]\ and a transverse
wave with velocity [ {p h4D7r2p,/r2} /(p f Ap,)].
These velocities vary with the period of vibration in a manner which
agrees, at least approximately, with experiment. It is clear that the
coefficient A is positive, while the experimental fact that the velocity
increases with the period shows that D is negative. The condition that
A is positive merely implies that the ether tends to move the matter
particles in the same direction as it moves in itself.
If we suppose that the medium is not isotropically symmetrical, while
at the same time it is such that the expiessions retain the same form when
two of the axes are turned through a small angle about the third, then
terms B ( — _) come into the value for U, and these, it is shown^
\ dz ay J
would cause the medium to produce rotation of the plane of polarisation
of a plane polarised ray traversing it. This rotation would vary approxi
niately inversely as the square of the period, in accordance with the law
discovered by Briot. By introducing higher differential coefficients into.
ON OPTICAL THEORIES.
215
the value of U in terms of u, etc., it is shown that these approximate laws
become, respectively,
=v„^(i + ^;+i;; +
(4)
V being the velocity, and Vq, £, etc. constants, while for \p, the rotation
produced by a length z of the substance, he finds
^=H
1 +
f f"
o * 4 '
(5)
For the explanation of double refraction Boussinesq supposes that the
constants in the above formula giving U, V, W in terms of u, v, w may
be functions of the direction of displacement ; but, arguing from the
relative importance of A, C, and D in the ordinary theory of refraction
(refraction is due to the existence of A, dispersion only to that of D), he
supposes that we may to a first approximation treat C and D as constants,
while we consider A as a function of the direction, and write for the
three axes of symmetry, the existence of which is assumed, the values
A(l + a), A(l + /3), and A(l + y).
This leads to the equations —
i'=K(l + .) + L(l + «)v'„
4!£
cPw
K(l + 6)f + L(l + h)^'v
ax
:K(1 + C) ~+U]. +C)V^W
ax /
(6).
K, L, a, 6, c being functions of the other constants. It is clear that
these are the same equations as were given by Lord Rayleigh,* and
■which have been already considered. The wave surface they lead to
is not Fresnel's, at least if we suppose the vibrations to be necessarily
transversal.
By retaining the terms involving the coefficient B, the elliptic polari
sation produced by quartz in directions oblique to the axis is explained.
The formula for the difference in velocity in the two elliptically polarised
waves traversing the crystal in any given direction agrees closely with
that given by MacCullagh. In this case the squares of the velocities parallel
to the axis are given by the expression N f 1 ± — r^ J , while the ve
locities in a direction making an angle with the axis depend on the
equation
w = N + — pr — sm'' t) + — —
± a/[(M  N)2 sin^ 9 +^^ I 2N + (M  N) sin^ j 1 . (7)
> See p. 179.
216
EEPORT — 1885.
wbicli can also be expressed in terms of the principal velocities at right
angles to the axis, for if w,, wj be the valnes of these, we have
M + N = io,^ + u}'
(M  N)2 = (o
2\2.
')
(w,2 + Wo")
(8)
The laws obtained in this paper are further developed in a second
and third in the sanae joui'nal. In this third paper, Bonssinesq ' points
out the necessity of including in the expression for U in terms of u
diflFerential coefficients of u, v, iv with respect to the time, and shows
that the phenomena of magnetic rotation can be accounted for by putting
in the case of a wave travelling parallel to z —
U =Au
dt
V = A^ + 33 '~
dt
W=: Aw
(9)
while the phenomena presented by refraction at the surface of a moving
body are explained on the supposition that in finding d?\] jdP we have to
take into account the visible motion of the body, and write
d
dt \
d , T d
— + JU — 
dt dx
+ M f +
ay
o
(10)
L, M, N being the components of the velocity at the point x, y, z ; it
is shown that in cases in which L, M, N are small compared with w',
the apparent velocity of light in the body is
o' = w +
2 ' '
yu being the refractive index and V the velocity of the body in the
direction in which the light is travelling. This, of course, is the formula
given by Fresnel.
§ 3. M. de St. Venant,^ in the article already quoted, sums up his criti
cism of the theory as follows : ' Les deux hypotheses principales de cette
theorie nouvelle me semblent bien pres de s'elever a la hauteur de choses
demontrees.' At the same time tbere remains the difficulty pointed
out by Sarrau ^ of explaining on mechanical principles how the various
terms in U, V, W arise, and on what physical phenomena the mechanical
forces brought into action depend.
§ 4. A further step in the progress of the theory was brought about
by the discovery of anomalous dispersion by Christiansen ■* in 1870. Le
' Bonssinesq, Liouville's Jounml, t. xiii. pp. 340, 425.
 De St. Venant, ' Sur les diverses methodes de presenter la th6orie des ondes
lumineuses,' Ann. de Chimie, t. xxii.
' ' Theorie des ondes lumineuses,' Ann. de Chini. (4), t. xxvii. p. 272.
* Fogg. Ann. t. 141, p. 479 ; t. 143, p. 250.
ON OPTICAL THEORIES. 217
Roux ' had found that vapour of iodine refracted red light more strongly
than violet, and Christiansen, in the paper quoted, announced the result
that for a solution of the aniline dye fachsin in alcohol the refractive
index increases from the Fraunhofer line B to U, then sinks rapidly as
far as G, and increases again beyond. The experimental investigation of
the subject was continued by Kundt,^ who proved that this anomalous
dispersion was marked in all substances showing strong surface color
ation, and that there was an intimate relation between it and the
absorptive power of the substance. As the result of his experiments,
Kundt was able to lay down the rule that in going up the spectrum,
from red to violet, below an absorption band the deviation is abnormally
increased by the absorption, while above the band the deviation is
abnormally decreased. Kundt has been able to see this abnormal effect
produced by the absorption of sodium light.
On the old theory of dispersion, as developed by Cauchy and others,
this effect was inexplicable. Boussinesq, it is true, had explained the
phenomena in vapour of iodine by saying that it implied that the co
efficient D was positive ; and here, in a way, lay a germ of the truth, for
the mutual reaction theory lends itself readily to a partial explanation of
the whole.
§ 5. Such an explanation was first given by Sellmeyer. He had
been led to expect the effect from theoretical reasons in 1866,' and had
endeavoured to discover it in a fuchsin solution, but without success.
The action between the ether and matter is a periodic one of the same
period as the light wave traversing the ether. Owing to the enormous
density of the matter compared with the ether its motion will in general
be negligeably small ; but if it should happen that the period of the
natural vibrations of the matter particles coincides with that of the
incident disturbance this will no longer be the case. The energy of the
light vibration will be absorbed by the matter, and this absorption will
tend to react on the lightdisturbance, and will, it can be shown, increase
the refractive power of the medium for disturbances of greater period
than the critical one, and decrease it for disturbances of less period.
The problem is much the same as that of a pendulum the point of
.support of which is undergoing a small periodic disturbance. If the
period of the disturbance be greater than that of the natural vibration of
the pendulum the reaction of the pendulum on its support will tend to
quicken the motion of the latter, and vice versa.
Sellmeyer, in the papers referred to,^ published in 1872, after a most
clear and able discussion of the difficulties of the elastic solid theories,
adopts the hypothesis that the ponderable atoms vibrate, but with much
smaller amplitudes than the ether particles. He then proceeds to consider
the mechanism by which this is brought about. As with Boussinesq, the
ether is supposed to have the same rigidity and density everywhere. The
ether particles act directly on the matter particles, and in consequence of
the vibrations of the former the equilibrium positions of the latter are
' Ann. de Chiiii. S. III. t. xli. p. 285.
= Poffff. Ami. t. 142, p. 163; t. 143. pp. 149, 259; t. 144, p. 128; t. 14.5, pp. 17
and 164.
^ Sellmeyer, Por/ff. Ann. t. 142, p. 272.
■* SeUmeyer, ' Ueber die dxirch die ^5i;tlierSchwingungen erreg^en Mitscliwingungen
der Korpertheilchen und deren Kiickwirkung auf die erstern, besonders zur Erklarimg
der Dispersion und ihrer Anomalien,' Poffg. Ann. t, 145, pp. 399, 520; t. 147, pp. 386,
£25.
218 BEPORT— 1885.
disturbed and execute small harmonic vibrations ; but the matter par
ticles themselves vrill not generally coincide with their positions of
instantaneous rest, and so we have to consider their vibrations about these
positions. The equilibrium position of the matter at any instant is made
to depend on the configuration of the ether at that instant, and may
clearly be expressed, under the given circumstances, as a simple har
monic function of the time, so that if soi Vo (o be the equilibrium co
ordinates at time < of a given matter particle of mass m', we may put
^u = «„ sin 27r ^ .... (liy
r
The ampUtude a^ will be very small.
The force acting on the particle m' is then considered on the assump
tion that the action between two particles of ether and matter respectively
depends solely on the distance, and may be expressed by mm'f(r), and it
is shown that, supposing that/(r) is a continuous function of the coordi
nates,' the force per unit mass tending to draw in' to its instantaneous
position of equilibrium is
X=^%^.^o) .... (12>
where c is a quantity depending on /and the configuration of the medium,
which may be a function of the direction. Thus, for an isotropic medium
we have as the equation of motion of the matter particles —
=  r^\^ ftflSin ^ + ci) ,
which leads, of course, to the integral
i=:^^aosm^(t+a) + hsm^l(t + ft) . . (13>
t' — c r
except when r^^, when
t, = — TT  ttQ COS ^(rLa) r 6sin ^ (t + l^) • • (14)
t d d
The question as to the legitimacy of the assumption involved in the
equation
tQ = ttg sin — {t + a)
T
is then discussed, and it is finally shown that it is correct.
Again, it follows with great probability, from the experiments of
Fizeau and Foucault ^ on interference with long difference of path, that in
a ray of light the amplitude of vibration resolved in a given direction is not
constant. We have, therefore, to treat a^ as varying — slowly, it is true,,
compared with the rapidity of the vibrations — but still, it is probable,
passing through many series of changes in one second.
This leads to the result that h, the amplitude of the natural vibrationa
' See Stokes, Srit. Assoc. ReiioH, 1862, p. 261.
"^ Ann. de Chim. s iii. t. xxvi. p. 138.
ON OPTICAL THEORIES. 219
of the matter particle, will always be small unless r = c. Omitting, then,
these from consideration, it follows that
_2
t' — c^
and the vibrations thus set up in the matter are shown to be the cause of
refraction ; while if r = c we have
^= —a cos 2:7 ,
da_. ^ . . . . (16).
and these vibrations are the cause of absorption.
So far, then, the results of this investigation agree with those
Bonssinesq has given. They are, however, more general, in that they
contemplate the possibility of the motions of the matter particles becoming
appreciable, and so producing absorption. The next paper considers the
question of the manner in which the action between the matter and ether
aflects the velocity of light. At 6rst the direct efPect of the matter on the
ether is neglected, and the refractive power of the substance is found by
considering the energy lost by the ether and gained by the matter in each
vibration. The refractive power is measured by n'^ — ], where w is the
refractive index.
Now consider a volume so small that all the ether particles in it
may be treated as in the same phase, so large that it contains many
matter particles, and suppose the reactions considered confined to the
ether and matter of this element.
Then it can be shown that if m' be the density of the ether, a' the ampli
tude of its vibration, the energy lost by the ether is (n^ — l)2x'^m'a'yT'^,
while that gained by the matter is 2Tr'^ [Imr'^at)'^ J(t^ — c^)] jr^, whence the
important formula
r.2
SJ/lr Mn^
„.! = ^^!:i .... (17).
is obtained.
We may write this —
,2_1 V
1=Z
r 1 <^«>
where by E we mean that all the possible values of S, the free period of the
matter particles, are to be taken into consideration. Now let us suppose
that r is greater than c, and that the matter particles have only one free
period, then the denominator of the fraction is positive, and decreases as
r approaches c. The refractive power, therefore, increases as the period
decreases (i.e., as we go up the spectrum), and as t approaches the critical
value c (i.e., as we near the absorption band) the refractive power is
abnormally increased. Above the absorption band, supposing there be
but one, the fraction is negative, and decreases numerically in value as r
is still further decreased ; and until r reaches a value for which l/r^ =
l/o^ + K, n is imaginary.
^^^ EEPOKT — 1885.
As r decreases Still further the refractive power increases, but the
refractive index is less than unity.
The presence of a second absorption band above the first will of
course, modify the conclusions. The change in refractive power is
perhaps best illustrated by a curve, as is done in Sellmeyer's paper For
the case above considered take values of the refractive power (n'l)
tor ord.nates and the reciprocals of the periods for abscissfB, then the
equation in the case of one absorption band will be
where a = i/c^
Thus the curve is an hyperbola, with the axis of .r and the line a; = a
as asymptotes. If there be two absorption bands we have
K , L
y= — +i^.
a—x b — X
and in this case there would be two critical values for x (viz., a and h) for
which the refractive power would become infinite, and near which the
dispersion would be anomalous.
In 1874 there appeared a paper by Ketteler i on the same subiect.
the^fm^muir' ''^^^'" enunciated as the law of dispersion in a gas
n^} = ^
0'
1
I being the wave length and o, ft constants.
I^urther comparison with experiments had led him to the formulaj
l=Kr + A+ — ~
and he now shows that by a proper interpretation of the constants this
wilJ include the case of abnormal dispersion,
§ 6. The theory of the mutual reaction between the matter and ether
was next developed by Helmholtz, and his work was continued by
Loramel, Ketteler, and Voigt. The method adopted by Ketteler differs
somewhat from tiiose of the other three. Helmholtz ^ (in 1875), LommeP
(m I87&), and Voigt » (in 1883) start in the same manner to form the
simultaneous equations satisfied by the displacements of the ether and
matter particles in a given element of volume. Let n, v, w be the dis
placements of the ether particles of density ni in an element of volume cv,
U, V, W those of the matter particles of density ^i.
The forces on m are, as in Boussinesq's paper referred to above,^'
■considering only the components parallel to the ,«axis :—
Ar,l, ^f^^}t^''^^^^lT'H^^^?''^^^^ aer sogenannten anomalen Dispersion,' Paw.
^WM. Jubelband, p. 166. See also p. 181.
\ Helmholtz, ' ZurTheorie der anomalen Dispersion,' Pog,/. A^m. t. 1.5i, p. 582.
p 339 Theorie der normalen und anormalen Dispersion,' ^ned. Ann. iAii.
* ^oi&t, Theorie des Lichtes fiir vollkommen durchsichtige Medien,' Mied. Ann.
X, Aix. p, o7o.
* See p. 213.
ON OPTICAL THEORIES. 221
(1) X', arising from external impressed forces ;
(2) X, arising from the action of the other ether particles external to
the element cv ;
(3) A, arising from the action of the matter.
"While for fi, the matter particle, they are : —
(1) S', arising from external impressed forces ;
(2) ^, arising from the action of the matter external to the element ;
(3) A, arising from the direct action of the ether.
So that the equations of motion for an isotropic medium are —
j^^ = X' + X +A. etc. 1
m'—rir = ^ + A + A,
dl^
etc.
(19>
a^'
In all three theories the impressed forces are supposed to vanish, so that
X' = S' = 0. The action between the matter and ether is supposed to
be confined to the element of volume considered — i.e. the dimensions of the
element are treated as large compared with the distance at which the
direct action of an ether particle on a matter particle is sensible.
This leads to the relation' J. + A = 0, independently of the value
of^.
The term X springs from the ordinary elastic reaction of the ether.
Helmholtz and Lommel, considering only a wave of displacement in the
direction of x travelling parallel to z, write for this term
while Voigt considers the general forms of the expression given by the
ordinary elastic solid theory, which, of course, reduces for the case of an
isotropic medium to
e V ^M + e' — ,
ax
where
5^ du , dv , dw
= — + — \ — .
fZ« dy dz
For the forces represented by S, Voigt again considers the general
case of a strained elastic solid, while Helmholtz and Lommel after him
write
>—l 9TT *> "' U
Tor the proper values to be given to A and A there is great divergence
of opinion shown in the three theories.
' In his paper Lommel — as has been pointed out byJKetteler, ' Optische Contro
^ersen,' Wied. Ann. t. xviii. p. 387, and "Voigt, ' Bemerkungen zu Herrn Lommel's
Theorie des Lichtes,' Wied. Ann. t. xvii. p. 468— really employs the condition ^  A = 0,
for he estimates « and U in opposite directions. In his reply, Wied. Ann. t. xix.
p. 908, Lnmmel endeavours to justify the signs used, but I think witliout success. The
effect will be to change the sign of a coefficieEt in one of the terms.
222 REPORT — 1885.
Helmholtz supposes, ' um die Bewegungsgleichungen zu vervoll
stjindigen,' that A is proportional to the relative displacement of the
ether and atoms in the element of volume, and writes, therefore,
A = /32(U ?0
Lommel supposes that the action ' follows Newton's law of friction,'
and depends on the relative velocity of the two ; he puts, therefore,
A^fi'^CUu).
at
The expression given by Voigt is much more complicated, and can
iDest be considered later. Thus the equations we have to deal with are —
(Helmholtz), and
,y=,j>(n„)«'uv'^;^
(20)
ctr dz^ dt
(I'll 9 aU , „)(l ,r~r >
(^2U ,.2''^TT ^ 2TT 2 ^?U*
(21)
(Lommel).
The method of solution is the same in both, xi and U, which, strictly,
are the displacements of ether and matter in the same volume in the dis
placed condition, are treated as if they were the displacements of ether
and matter having the same undisturbed coordinates «;, if, z. This is
legitimate, for U and n are both taken to be functions of the position of
the wave front and the time only, and hence for all points on the same
wave front U has at a given instant the same value.
Assume, then,
U = Ae''^ + '•'" '■"'■■tj • • • . (22)
k is the coefficient of absorption, c the velocity, and 2!r /« the period of
the vibration.
On substituting these values in Helmholtz's equations, we find
and
2^ _ /3*y'
en
o^T;: (fiH^ _a^_ ^32)2 + ^4,,2 = ^ (say) • . (24)
* In this equation tlie sign of 0 has been changed from that given by Lommel in
accordance with the remark on p. 221 ; but see Lommel's reply to Voiot Wied Inn
t. six. p. 908.
t A, of course, no longer has the same meaning as above, but is the amplitude of
the matter vibrations.
To solve these, pat
ON OPTICAL THEORIES. 223
]
 = 0 COS (t»,
c
h
 = p sm (.).
n
Then
1^=p'cos2w=f'
2^
= p^ sin 2w = G
(25)
Thus the value of Jc, on which the absorption depends, is proportional
to y^, the coefficient of (T\J jdt in the equation, and vanishes if y^ is zero ;
that is, if there be no frictional resistance to the matter motion. If h be
•at all appreciable, the lightdisturbance will penetrate but a little way
into the medium, so that for transparent media we may treat h, and there
fore G, as small.
In this case we have
,2 = F+^j^ + ,etc.,
while in the small term we may put for G/F the value 2A;c/w.
In these circumstances, then,
l=\..G^'y'
where
^,2 = a2 + /32_yt/2^]
(26)
(27)
Thus, as n changes kjc is a maximum when n = v; if the corresponding
values of k and c be Lq and Co, then
io I "^ 4^2(^2^ ^2) f^ • . . (28)
If the value of y be zero, then, for n = r, h is infinite compared with c ; all
the light is absorbed.
At the same time A is large, and we have, in dealing with the motion
of the matter particles, to consider the limit of Ae*o^.
Turning, now, to the refraction, let C be the velocity of light in free
space, N the refractive index, and suppose that the term ^G^/P may be
neglected, then
N2 = c^F = ^'" fl  — + /3^(^ + 2^^n^) [
a2 L mn^ m^w2{(,.2_ ^2^)2 + 4^2(^2 + ^2^1 J • y^y)
and the maxima and minima values of this expression lead to the limiting
values of the refractive index.
These, it is shown, are given approximately by n^ — v'^=±l 2)'«t, which
224
REPOBT 1885.
correspond nearly to the maxima of absorption. Thus, as we go up the
spectrum, the refractive power is a maximum for the value oi n, given by
7i,2 = ,/2 _ 2 rnr, and a minimum for 7.^ = r^ + 2)"Z3. There is, thei'efore,
abnormal dispersion in the neighbourhood of the absorption band, but
elsewhere the refractive index increases with n. Again, for large values
of 11. we have N2 = C^to/o^. Now, if the density and the rigidity of the
ether be the same in all bodies, we should have C^ = a^jm, and therefore in
this case 1^ = 1. Thus the light of shortest wave lengths would be trans
mitted without refraction, contrary to experimental results. Sellmeyer,
however, pointed out a method of explaining this difficulty which would
be consistent with t"he supposition that C^ is equal to a^jm. According
to him, we must suppose that there is a strong absorption band some
where just above the visible limits of the spectrum — that is to say, that
the value of i^ — 2i"st is just beyond the limits of the visible spectrum,
and that owing to this the refraction below the band is abnormally
increased.
The paper closes with a method for constructing the form of the
refraction and absorption curves.
Lommel's equations can be solved in a similar manner, and lead to
similar formulfe. The two theories can best be compared with each
other and with experiment by changing the notation slightly, and
adopting that used by Ketteler ' in his criticism of the same. Let us put,
therefore,
a =,
(30)
..<.. 5))
Then Helmholtz's equations (23) and (24) become
(
A2
m
B^O^^n^)
f.i,nn^{{ro'n^y +
nh'y^
K}.
(31)
and
2k m
B2,5K
en a^ fimn ((jq^ _ n^) + nh'^^K^}
(32)
and if we suppose X, X,, Xq to be the wave lengths corresponding to the
periods n, I'l, and vq, we find
B2 X;^ A\2_ _ ;^^~
BX2 , A"« X/VXo' J
L
f.tm X
2 X2
G =
m
jim X,"
"'(^0
+ K2
(33)
' Ketteler, 'OiDtische Controversen,' Wied. Ann. t. xviii. p. 387.
ON OPTICAL THEORIES. 225
while the ratio of the amplitudes is given by
B X2
^=^' /^/./'V . x., • ■ • m
/{(^O^S)
We can give a sort of physical meaning to the constants in these formulae
as follows : A, is the wave length of the natural vibrations of the matter,
freed from any action of the ether; Xq is their wave length on the suppo
sition that the action between the ether and matter is proportional to
the displacement, while the ether remains fixed ; while I'l and j'q are the
frequencies of these vibrations. B vanishes when there is no matter
present, and since the expression shows that B/m is a number, it is
probable that B will be proportional to the matter density ; while K is a
number on which the strength of the frictional retardation depends.
The quantity Xj, the wave length of the free vibrations (i.e. the dis
tance the lightwave travels in a natural free matter period) is immensely
great compared with X, so that A is small compared with % except in the
cases in which X does not differ greatly from Xq.
It will be seen at once that the formula for F, on which, when the
absorption is small, the refractive index depends, in terms of the wave
length is very complicated. I am not aware that any attempts have
been made to compare it carefully with theory.
In the cases in which K is small (i.e., for transparent media) Xq will
be an approximate lower limit to the wave length of the light trans
mitted.
If we integrate the equation given by Lommel's hypothesis, modified
so as to agree with the principle of action and reaction, we find
F*=^
«2
• (35)
where B' is a constant related to the /3 of Lommel's equations in the
same manner as B is to jp above. If, however, we take Lommel's ex
pression strictly, to which he still adheres,' the sign of the fractional
expression must be changed.
If we retain the negative sign the formula (35) fails to represent the
facts. Neglecting for a moment the effect of absorption, and supposing the
ether to be of the same rigidity and density as in free space, the square of
the refractive index will be rather less than unity for the longest waves ; it
■will then decrease to a minimum value, which will be positive, and then
rise rapidly through the absorption band, for which X = Xq, reaching a
maximum a little above the band, from which it will again fall. Absorp
tion efifects will only slightly modify these conclusions. Thus the
spectrum above the band ought to be more refracted than that below, and
except just near the band the refractive index should decrease as the
wave length decreases. This is fatal to the theory in this form. In its
* This becomes the expression given by Lommel on substituting B'/m — K = €=,
^i" \. B' =wi(K — €), and interchanging m and /x.
' Lommel, ' Zur Theorie des Lichtes,' M'ied. Ann. t. xix. p. 908.
1885. Q
226 KEPOBT— 1885.
original form it is not open to this criticism, and accounts for the facts,
bat its fundamental equations are hopelessly at variance with Newton's
third law, so long, at least, as we suppose the mutual reaction limited to
that between the matter and ether in the element of volume considered
— that is, so long as we may suppose that there are many molecules in an
element of volume. The original formula for dispersion leads to results
which, as Lommel ' has shown, agree fairly with experiment ; and by carry
ing the approximation a step further the agreement becomes closer still,
so that his fundamental equations might be taken as an empirical repre
sentation of the facts with some approach to the truth.
Voigt's theory differs from these mainly in the values assigned to A
and A and the methods by which those values are obtained ; and before
treating at length of it, it will conduce to clearness if we consider
Ketteler's theory, the results of which have considerable resemblance to
the two already mentioned, while the work itself is earlier than Voigt's.
§ 7. Ketteler ^ is the author of a large number of papers on this
subject, and the form in which he has presented his theory has varied
somewhat, though the central idea which he has endeavoured to express
has remained the same throughout. The idea seems to be as follows.
The exact expression of the action between matter and ether, the A and A
of the fundamental equations, is unknown to us, and we must therefore
endeavour to eliminate it from the equations. This we can effect by con
sidering the work done per unit time on the whole system, into which, of
course, the mutual reactions will not come, and equating it to the rate of
change of the kinetic energy. This alone, of course, will only lead to one
equation, and though in some of his work Ketteler appears to obtain two
out of it, this, as we shall see shortly, is done by the aid of an additional
hypothesis.
It is, however, not till some of the later papers that these views are
completely developed. In his first paper ^ he assumes that the action of
the matter on the ether is to increase its rigidity by the quantity ea, and
to introduce a resistance acp, where £ is constant for the medium and a is
some unknown function of its dynamical condition, while the forces on the
matter are a(£' v^p' + kV')> f' being the matter displacement, so that,
considering the motion parallel to x, we have for the ether
and for the matter \ . ■ . (36)
Arguments similar to those employed by Sellmeyer lead to the equation
N2l = ^ (37)
and on multiplying the first of the equations of motion by p, the second
' Lommel, ' Ueber das Dispersionsgesetz,' Wied. An?i, t. xiii. p. 353.
^ Since the above was sent to press, Ketteler has published his optical theories in
the form of a book, Theoretische Optik : Braunschweig, F. Vieweg und Sahn, 1885. The
fundamental equations are formed as indicated below (Equation 43), and the remarks
made in connection with that section apply.
' Ketteler, 'Versuch einer Theorie der (anomalen) Dispersion des Lichtes in
einfach und doppeltbrechenden Medien,' Carl Repertoriwrn, t. xii. p. 322.
»» ^7r= (« + «°) A + "^P
ON OPTICAL THEORIES. 227
by p\ we find that the condition (37) reqaires the coeflacient of a to
vanish separately, and we are led to the two equations
(38)
and these are the two fundamental equations of the theory, from which an
expression is found for the refractive index in terms of the wave lenoths
and constants, viz. : — °
N2 = N»^ +^v^ (39)
— 1
\'
wrhere the S must be taken to include the different kinds of matter
)articles m the medium. So far, at any rate, the theoretical bases ot
these expressions are no more secure than those of Lommel and Helm
holtz. Ihe dispersion equation, however, is much more simple than that
given by Helmholtz, and agrees well, as Kefcteler i has himself shown with
experiment.
A second paper 2 develops some further consequences and traces the
torm ot the dispersion curve in various circumstances.
In a third paper ^ the principles of the theory are stated and applied
to doubly refracting media, but the equations from which he starts the
same as those given above, only written with three coordinates— do not
express the physical facts which they are intended to do, and the theorv
deduced can only be considered as empirical.
A further attempt, based on this principle of energy alone, is made in
a more recent paper ' to establish two independent equations Thus the
ether mass in an element being displaced a distance ds, the matter mass
•as ; then the equation
'»i?*+'s^*' = «S* . . . (40)
IS supposed to express the law of the conservation of energy for the ether
motion ; it neglects entirely the forces on m' from the action of neiffh
ftouring matter. The conservation of energy principle alone will ^ive
but one equation when applied to the system, though it will of course
eliminate the unknown reactions between matter and ether
w,fl T^^'^ remarks must be made with regard to other papers ^"^ dealing
with the formation of the fundamental equations. The equations D of
tne last article referred to are only true on the assumption that the
' See p. 181.
Ann^^lioTv'm^ Zusammenhang zwischen Absorption und Dispersion,' P^^^.
breclSn Mit'tpl'n ''2''°"^/''i?''?'''^°^ und Absorption des Lichtes in doppelt
orecnenaen Mitteln, Pogfi. Ann. Erganzung, Band viii. p. 444.
5 ^^f 1 .'Su' I^^spersionsgesetz,' Wied. Ann. t. vii. p. 658.
AMd £r mJ ..?^n ^r ^^^o^'^^^iiden AnisotropenMittel,' Mo7iatsier. der Koniql.
t S n 387 KrwS '"' ^°^.i^' ^^ 'Optische Controversen,' Wied. Ann.
X. xviu. p. 387 , Erwiederung auf Herrn Voigt's Kritik,' Wled. Ann. Bd. xxi. p. 178
Q2
228 BEPOET — 1885.
reaction of the matter on the ether produces a force —m'C — ^* while
the action of the ether on the matter is expressed by a force — m C — ^•
and, indeed, in his most recent work on the subject ' he realises clearly
that the energy principle only leads him to one equation, viz. : —
m ^dp + m' — ^ dp' = e\7^pdp — icp'dp' . . (41)
e being the rigidity of the ether in free space — and then combines with
this a ' second equation relating to the special mode of action of the
matter particles, which can be no other than the renowned fundamental
equation of Bessel's theory of the pendulum ' ; this may be written
It is then further assumed that the matter particles exert a force /jm'p'
on the ether, and the equations finally become —
»i§m'Co^'=evV+A»y
111
'c f^V , ,„/ dy _ /,,„/ : ., <ip'
C
dt
. ,dy ( , . dp'\
(43)
leading to the equation
N^Ki =
N^^ No'+Vl(Nl l)K^'
~\
,^iwikA
(44)
■where K is a quantity depending on y. When K is small, as is always
the case in transijaient media, this becomes the formula already men
tioned, which has been tested over so wide a range by Ketteler. It is
clear from these last equations that the action of the matter on the ether
is represented by ?)i'Co'ri + P^i'p', and of the ether on the matter by
in ^ T^ jg (Jifficult to conceive of the mechanical principles which
° df^'
would lead to these terms as they stand, and the occurrence of the
imao^inary quantity in the expression for the refractive index, to which
they lead, is a blot on the theory.
§ 8. In fact, the form of the equations given in his earlier papers ^'
leads to results which are more directly intelligible, while the equations
themselves can, it seems to me, be established by the aid of a suggestion
due to Ketteler himself (' Eine dritte Annahme,' p. 397).
For, taking the notation employed when considering Helmholtz and
* In Ketteler's paper ^, ' are used for the displacements. I have retained p, p', in
accordance with the notation aheady employed.
' ' Zur Dispersionstheorie des Lichtes,' Wied. Ann. t. xxi. p. 199. See also
Ketteler, TheoretiscJie Ojdilt, p. 85, et seq.
' Ketteler, ' Optische Controversen,' Wied. Ann. t. xviii. p. 387.
ON OPTICAL THEORIES.
229
Lommel, let us assume, according to this third supposition of Ketteler's,
that the reaction between the ether and matter is proportional to the
relative accelerations of the two. Helmholtz supposes it proportional to
the relative displacements, Lommel to the relative velocities. In this
<jase, then,
and hence
A=/3^J^(.U),
m5^+/32^^(t,_U)=.N,
<P
Thus
7)1
iVy, _ fihn d^XJ _ mX
■n
7W. + /32 dt^ m + /32
2 ,lfi ^ / ,7/2 — .. _ ,'2
df'
dt^
PP'
(45)
(46)
And, with Ketteler's assumptions as to the forces X and ^, these may be
written as follows —
dn „,
d<2
.(Pu
dz^
(....f)j
(47)
which are the same in form as Ketteler's equations, though a^ is not the
rigidity of the free ether, while there is a relation between C and C, for
and
C'='^.
c =
fi m + jy^
ft'
(48)
However, this does not matter, for it is the product CC which comes
into the fundamental equations of the solution, and we find
2
1 72 in
L. °(^0
(
1)%K^^^
A,^
2k VI y
en
DK?
K2
^2
(49)
(50)
where D = CC, and K is proportional to y^.
The quantity a^/m is no longer the square of the velocity in free
space, and cannot be put equal to unity, and, in fact, a'^/vi will be the
square of the refractive index for very long waves. Ketteler (p. 398)
230 EEPORT— 1885.
seems to consider it an objection to Lis theory that it gives a value dif
fering from unity to the refractive index for infinite waves, but the objec
tion is not, I think, serious. As has been stated before, the dispersion
equation given by his theory has been repeatedly tested by Ketteler,'
and the agreement between theory and experiment is very satisfactory. .
Thus we may probably look upon this equation as one established em
pirically by his experiments, and while not agreeing with the reasoning
employed by Ketteler in forming his equations of motion, may see in
those equations the expression of a possible law of action between matter
and the ether.
§ 9. Let us now turn to Voigt's work, which is of more recent date.
He has been a severe critic of his predecessors, and objects strongly to
various points in their work.
In his first paper ^ on the subject Voigt, following Boussinesq,^
remarks that mtVuliW and /jid^U Idi^ being quantities of the same order,
U will be very small compared with u because fi is very large compared
with m ; it is therefore not necessary to introduce terms involving U
into the diiFerential equations for u. To this we may reply, (1) that it is
quite possible that the coefficients of U and its differential coefficients
involve fi the matter density, and that in consequence the terms in ques
tion are comparable with md^itjdt^, and (2) that in the critical case
near the absorption band the value of U becomes large, and may be
quite comparable with ii.
Voigt also objects to the form adopted for S in all the previous
theories, viz. — (kU + ydV jdt), pointing out that Helmholtz introduced
the kU ' zur Vereinfachung der Rechnung,' and the ydV/dt to explain
the transformation of lightenergy into heat. If the ponderable matter
is to be looked on as an elastic solid, then, according to Voigt, we ought
to put for S terms like cr \7 ^U + b^dS f dx. To this Lommel replies*'
that the matter molecules each as a whole are not affected by the pas
sage of the wave of light, but that intramolecular or atomic motions are
set up, and that the forces arising from these are represented by his
terms, how he does not explain.
Of course, since it is assumed that U = Ae''^*'"^''"'^'",.
V^U= — {h + iy;/c)U, the difference between the two will only show
itself in a change in the refraction formula.
The main criticism * of Ketteler's work relates to the method in which
the equations are obtained. To this we have already referred.
§ 10. After these criticisms we turn to the consideration of Voigt's ^
own theory. His fundamental equations are, as we have seen,
' Ketteler, ' Constructionen zur anomalen Dispersion,' ^]'ied. ^1««. t. xi. p. 210;
' Einige Anwendungeii des Dispersionsgesetzes auf duichsichtige, halbdurchsichtige
und undurcbsichtige Mittel,' Wied. Ann. t. xii. p. 363 ; ' Experimentale Untersuchung
iiber den Zusammenhang zwischen Refraction und Absorption des Lichtes,' Wied.
Ann. t. xii. p. 481 ; ' Photometrisclie Untersuchungen,' Wied. Ami. t. xv. p. 336.
" ' Bemeikungen zu Herrn Lommel's Theorie des Lichtes,' Wied. ^M7i. t. xvii.p. 468.
» Seep. 213.
* Lommel, ' Zur Theorie des Lichtes,' Wied. Ann. t. xix. p. 908.
^ Voigt, ' Ueber die Grundgleichungen der optischen Theorie des Herrn E.
Ketteler,' Wied. An7i. t. xix. p. 691 ; ' Duplik gegen Herrn Ketteler,' Wied. Ann. t. xxi.
p. 534; Ketteler, ' Erwiederung auf Herrn Voigt's Kjitik,' Wied. Aim. t xxi. p. 178;:
' Duplik gegen Herrn Voigt,' Wied. Ann. t. xxii. p. 217.
" Voigt, ' Tlieorie des Lichtes fiir vollkommen durchsichtige Median,' Wied. Ann..
t. xix. 13. 873.
ON OPTICAL THEORIES.
231
■ (51)
X' and S' are each put equal to zero, and the condition A + A = is
assumed ; that is, it is supposed, as we have stated before, that the sphere
of action of each ether particle on the matter is small compared with the
dimensions of the element of volume considered.
An expression is then found for the rate at which work is being done
on the compound medium, and the condition formed that this expression
should be a function of the time only.
So far as the terms depending on the mutual reactions are concerned,
the rate of increase of the energy is given by
s;=.p(™..)„(A'?(^.B.!0:^).c*^))
+ S j d (surface) Afc 8/,^,. = J (vol.) + J (surface)
(52)
where the S implies that more than one medium may come into con
sideration, and the integrals are to extend over the whole volume of each
separate medium and all the interfaces between the media, these being
indicated by J (vol.) and J (surf.) respectively.
Forms are then found for A, B, C which make J (vol.) a complete
differential coefl&cient with respect to the time, and at the same time lead
to linear equations of motion which admit of solution in the form
u = '^Ae^'' *'""'*' "~ * '''\ Four possible forms are found, which are given
below.
(1)  A, = «i(it  U) + 03(1'  V) + 0^(10  W)
/ox A d(vY) d(w  W)
(2) A,=p, ^ ^^^ ^ p, ^,^
dt
(3) A, = r,
d2(«_U) , d^ivY) d^(ivW) h ■ (^3)
dt^
+ s
df
+ S2
dt^
(4)
_ d^(vY) d^wW)
23
dt^
df^
It will be noticed that (1) gives us Helmholtz's theory ; (3) gives
us Ketteler's in the modified form I have suggested ; for an isotropic
medium it is shown that the coefficients and s vanish. Lommel's form is
not included in the above ; it is therefore, we see, inconsistent with the
conservation of energy in the medium.
But there are other terms in the volume integral J (vol.) which will,
when combined with suitable terms in the surface integral J (surf.), make
the whole up to a differential coefficient of the time.
These terms are given by
A =
dK
dx
dij
dA,
dz
(54)
232 EEPOET— 1885.
etc., and lead to terms in the volume integral
d (volOrA.. ^^(J^) + A„ i^X!i^) + A. ^^!(!i^U) + . . 1
L dtdx " dtdu ' dtdz ^ • • • I
■= ^ (let us suppose) . (55)
Then /' is a function of ^^"~ , etc., and four possible forms are found
for A^, etc., viz. putting x, etc., for the difiPerential coefficients
dJuV)^ etc.
dx
(5) /'j, a homogeneous function of xi . . . X9
(A,).5 = 'p',etc.
Thus — A,, = Em, ,. x , etc.,
with n^=n^;.
(6) A. = 2^.,% etc.,
dt
with the conditions p,, = 0,
giving /g = constant.
(7) A Sr ^*X.
with ?,j = »v,,
(8) A, = ^,,^.
with2,.i=0, qu=qj;,
and /' = SSg,/^ ^'_^ixA
We have thus eight possible forms of values for A, etc., all or any of
which may occur in the equations. In the equations for the ether,
U, V, W, being very small compared with ii, v, w, are omitted.
An isotropic body is one in which no one direction differs in its
properties from any other. For such a body it is supposed that the forces
defined by 2, 4, 6, and 8 above do not exist, and a, a' being the
coefficients in 2/'^ and  2/'^ respectively, it is shown that the equation
for plane waves travelling parallel to z is —
ON OPTICAL THEORIES. 233
and hence,
1
m{e
> + «)
e
4aV2
\2
s^
m
+ r
n\^m
4eir2
X being the wave length in air and N the refractive index.
The complete valne for A is —
.._/i(^J2,..n^),.*ii=n)_.0.^) .(57)
and in the above equation (56) U has been treated as small compared
■with u.
We see that the first and last terms are those given by the theories
of Ketteler and Helmholtz respectively ; Voigt's more general theory
includes them as particular cases. The first and third terms occur in the
theory developed by Boussinesq, which is also included in Voigt's.
In a further paper, in reply to some ciiticismsof Lommel, who argues
that a wave propagated through the molecules of the medium must be a
BOundwave, and that therefore the matter motion which affects the trans
mission of light must be i'7?iramolecular not «(<ermolecular, Voigt
shows,' by taking the matter motion into account, that the velocity of wave
propagation in a medium constituted as supposed will be given by a
quadratic equation. One root of this quadratic will be comparable with
the velocity of light in this medium, the other with that of sound ; while
the ratio of the energy of the matter to that of the ether in the light
motion is the reciprocal of the same ratio in the soundmotion.
Voigt's theory applies only to perfectly transparent media, and its aim is
to show that the optical properties of all such media can be explained on
an elastic solid theory by considering the mutual reactions of two
mutually interpenetrating elastic media. The author does not touch the
problem of absorption, because for that purpose we require to deal with
the molecular motion to which, in his opinion, heat effects are due, and
these lie outside the domain of elastic solid theories. He does, however,
deal with double refraction, circular and elliptic polarisation, and the
various problems connected with reflexion and refraction. Most of these
have been treated of also by Lommel and Ketteler.
Chapter II. — Double Refeaction.
We will consider first the problem of double refraction. All three
explain it in a similar manner. Within a crystal the action of the
matter particles on the ether will depend on the direction of vibration,
and some or other of the constants of the theory will be functions of this
direction. It is assumed that the ether remains isotropic, and that there
are three axes of symmetry, which are taken as those of the coordinates.
§ 1. Lommel 2 in his theory treats the constant we have denoted by
a^ as a function of the direction, ft'^, which determines the action
between ether and matter, and y^, on which the frictional effects depend,
' Voigt, ' Zur Theorie des LicMes,' Wied. Ann. t. xx. p. 144.
* Lommel, ' Theorie der Doppelbrechung,' Wied. Ann. t. iv. p. 55.
234 REPORT— 1885.
are left invariable, so that the ether equations remain unaltered, and the
matter equations become —
and similar equations with a^ and a^. It has been shown by him that
for a transparent medium the velocity is given by 1/r, where r is a
radius, drawn in the direction of displacement of the surface — 
(^^ + 2/^ +^^  1) ( ^ti + N;ti + NT^i) =«=^ + 2/^ + ^^ (59)
and the directions of vibration are the axes of a section of this surface by
the wave.
These results are at variance with experiment, which requires that the
wave surface should be that of Fresnel, and no reason is assigned in
the paper for making a? rather than /3^ or y^ a function of the direction.
Circular polarisation and the rotation of the plane of polarisation '
are also treated of by introducing into the equation for U the term
— 2/111 cos aj , and into the equation for V, 2u2 cos a , where I de
dt at
pends on the strength of the magnetic force, and a is the angle
between its direction and the axis of z.
From this it follows that the rotation is proportional to
and the results of calculation agree fairly well with Verdet's experiments.*
For the rotation of sugar terms of the same kind, but without the
cos a, are introduced.
It has been shown long since, by Airy,^ Neumann, and MacCuUagh,
that such terms in the equations would lead to results in fair agreement
with experiment, and Lommel does not attempt any other justification of
their existence than that the results they lead to are in agreement with
experiment. Similar remarks apply to his paper on the properties of
quartz,'* in which the same terms are added to the differential equations
already found for a crystalline media. The two waves travelling in any
given direction inclined at an angle 6 to the axis are elliptically polarised.
The elliptic paths of the particles are similar ; their ratio is given by —
^ 6 8in2 0+ {62 8in<0 + <^o^cos''e]^ ' • ^^'
and the difference of phase between the two by
^2 = J2 sin4 a + (^^2 cos" fl . . . (61)
where h and dg ^.re functions of the refractive indices and wave lengths.
The axial rotation is given by —
Q = c i^'/) ' .... (62)
' Lommel, ' Theorie der Dehnung der Polansationsebene,' Wied. Ann. t. xiv. p. 523.
2 Verdet, Ann. de CUm. (3), t. (59, p. 471.
' Airy, Phil. Mag. June, 1846 ; Neumann, Die mai/netischen Belmnngen, Halle,
1863 ; McCuUagh, Roy. Irish Trans.
* Lommel, ' Theorie der elliptischen Doppelbrechung,' Wied. Ann. t. xv. p. 378.
ON OPTICAL THEORIES. 235
These results are all in close agreement with experiment.
In another paper ' this formula is carried to a higher degree of ap
proximation, and redaces to Q, = ^ — — — ^. This agrees well with the
measurements of Soret and Sarasin, between the wave lengths 7604 and
2143.
§ 2. Ketteler's contributions to the theory of double refraction have
been very numerous. Most of the papers already mentioned, contain
something on the subject. The theory given in the first of the papers
mentioned is in its fundamental principles in close accordance with that
developed by Lord Rayleigh in 1871, though the equations given on p. 95,
following Von Lang, as representing the motion in a crystalline elastic
solid are incorrect. In it a distinction is drawn between the displace
ment normal to the ray, which leads, it is said, to equations of the form —
(m + mj^^+^=a'^ht . . . (63)
at dx
and those in the wave front, for which the equations are —
^"^■^i^^S) =''"' ■ ■ ■ (•=*)
The arguments by which the second equation is deduced from the first
are somewhat obscure ; they are, however, further developed in a later
paper.3 The ray direction is defined as that in which the energy of the
vibration is propagated, and the direction of vibration is normal to this.
The fundamental equations of this theory have already been given.*
They are, in their final form,^
. (65)
where the constants Cq, /3, k and y may all be functions of the direction.
It IS shown in the paper (' Optische Controversen ') now before us that the
conditions of incompressibility require that Co, k and y should be constant,
so that the theory turns entirely on the variability with the direction of /3,
or rather of C, which is connected with Cq by the equation—
C' = ^^.Co (66)
<■ n '^^^^ ^^ ^^*^^ ^° *^® groundwork of the theory, for in its form in the
Optische Controversen ' it is assumed that C and Cq are unconnected.
1 he paper ' Zur Dispersionstheorie ' starts wdthout the term in /3,
arriving at the equation C + Co=0, and then (p. 208) inserts the /3 ' in
^ ' Lommel, ' Das Gesetz der Eotationsdispersion,' Wied. Ann. t. sx. p. 578.
■• p. 179 ; and also Ketteler, ' Zur Theorie der Doppelbrechung,' Wied. Aim.
A t!™; ^; V ' ^^^°"e <^er absorbirenden AnisotropenMittel,' MonatsUr. der Konigl.
Aitad. der Miss, zu Berlin, November 13, 1879.
! ^etteler, 'Optische Controversen II.' Wied. Ann. t. xviii. p. 631.
* See p. 228.
* Ketteler, ' Zur Dispersionstheorie des Lichtes,' Wied. Ann. t. sxi. p. 199.
236 BEPORT— 1885.
order to explain experimental results.' Introdacing the term C, as
defined above, the equations become —
(67)
These equations will not lead to satisfactory results.
Circular ' and elliptic polarisation are also treated of by Ketteler, and
are explained on the supposition that terms of the form — Av + %^\
come into the equation for U, and terms + (l\} + g^") into that for V.
The rotation in a magnetic medium is given by ti = ir p ~ ' ^ N being
the refractive index, while the value of N in a crystal like quartz may
be found from the formula —
W\ = (N,2 _ 1) (1 + cos^fi) + (Na^ _ 1) sin2 « ± [(Nj^  ■^^^) sin*
+ 4fc2A2cos2 0(N,2_l)(N,2cos2« + N22sin2<9l)]'. . (68)
Ni and Nj being the refractive indices at right angles to the axis, and A;,
a constant on which the rotatory power depends. For ordinary active
media the law of the rotation is
" = a+^2 + ;^4 + .etc. . . . (69)
It will be noticed that in the theories of both Lomrael and Ketteler the
rotatory terms are introduced into the equations of the matter particles,
and affect the ether only indirectly through the values of «, v, and w.
§ 3. Voigt's work ^ embraces double refraction and circular polarisa
tion. The existence of three principal axes is assumed, and for these the
coefficients o and s in the values of /j and /,* of equations (53) vanish.
The values of /^ and/7 are written down with coefficients a^, aj, etc., and
a,', tta', etc., respectively, and finally the equation of motion for u is
obtained in the form —
"*" ^"^ + ^'^ ddy + ^'^ + ^^J^z "^ £ [similar terms with a/, etc.] (70)
It will be seen that there are enough coefficients here to give any
imaginable theory of double refraction.
Put m + r, = «i,, etc. Then the equations may be written
> Ketteler, ' Theorie der circularen und elliptiscben polarisirenden Mittel,' Wied.
Ann. t. xvi. p. 86.
" ' Theorie des Liclites fiir vollkommen durchsichtige Median,' ]\'ied. Ann. t. xix.
P 873. * See p. 231.
ON OPTICAL THEORIES. 237
Where A, = A, + A/— 5, A; and A,' being functions of a, h, c, etc., and P
ar
cLtt
is a linear function of p and the differential coefficients ^, etc.
ax
The equations in this form may be compared with Green's, which differ
from them only in the facts that his coefficients of drujdt^, cPy /dt"^, and
d'^z/dt'^ are the same, and his other coefficients are independent of the
time. Voigt's equations, in fact, include both Green's and those given by
Lord Rayleigh.
Let r be the period of vibration, and denote ?h, — n^T by Tj, etc. ; then.
it is shown that if we assume the relation — + —  + — = 0, in order to
ax ay dz
obtain Fresnel's wave surface at all the condition T, = T2 = T3 = Tia
necessary.
These equations being satisfied, the other relations required to give
Fresnel's construction on either assumption as to the connection between
the plane of polarisation and the direction of vibration are those given by
Green, with the addition that since in Voigt's coefficients the period is
involved, and since Fresnel'a construction holds for all wave lengths, each
of Green's relations splits into two.
A difficulty as to the meaning of the constants leads Voigt to prefer
Neumann and MacCullagh's theory as to the position of the plane of
polarisation. To obtain Fresnel's original construction it is necessaiy to
suppose B]2 to be different from B21, and this would imply that elastic
reactions are bi'ought into play by rotating an element of ether as a whole
without dilatation ; that, in the ordinary notation of elastic solids, T,j^ is
different from T,j,. If we treat this as out of the question, then B12 must
be equal to B.,], and Fresnel's original construction for the plane of polari
sation is impossible.
Circular polarisation is explained by the terms introduced by/2, /4,/g,
and/^ of above,' but the terms to which /j and /g would give rise are
omitted as not necessary to explain any known phenomena, and the
equations in an isotropic medium become — ■
, , .d'^U f , ^dHl, . , d^U , dv , p'dH /^,n^
(.^ + 0^2 = («),^+«;p^.' + ^^+<7^, • (72).
etc. ; the rotation produced by a thickness c of the medium will be —
Q.—
!V(e + a)(m + r
)V rvJr'^2(e + a)r2J
The same terms are then applied to a crystal, and the case of a uniaxial
crystal such as quartz is worked out in full.
The equation to determine the velocity in a direction making an angle
6 with the axis is found to be —
a and h being the velocities at right angles to the axis.
This paper then gives a consistent account of the propagation of light
in all known transparent bodies. We proceed to deal with the problem
' See p. 231.
238 REPORT— 1885.
of reflexion and refraction on this theory, and after that to make some
general remarks on the whole.
Chapter III. — Reflexion and Refeaction.
§ 1. Lommel, so far as I am aware, has not considered the problem
of the reflexion and refraction of light on his theory. Ketteler, however,
has discussed it in many of his papers.
In one of the earlier papers ' the fundamental principles on which he
intends to work are laid down. They ai'e as follows : —
I. The conservation of energy.
Ila. The continuity of the stress pai'allel to the surface of separation.
116. The continuity of the component of the force on an element
resolved normal to the surface.
III. The continuity of the displacement resolved along the surface.
The reasons given for 116. in place of the correct principle of the
continuity of the stress normal to the surface are not very clearly stated.
No assumption, except such as is implied in I. and III. combined, is
made as to the displacement normal to the surface.
The principles are then applied to the general problem, but in express
ing them in symbols, except in the case of I., the motion of the matter
is entirely neglected. Thus the stress considered in II. is only that
arising from the action of the ether ; the part which springs from the
reaction of the matter is omitted from consideration. Again, in forming
the equations connecting the amplitudes of the incident reflected and
refracted rays, 116. is not employed.
Ketteler's work, then, in this paper is not really specially connected
with his theory of the mutual reaction between the ether and matter. It
is rather a modification of Fresnel and Green's work, for which there
can be no justification assigned. The problem of metallic reflexion is
discussed, and in a second part ^ of the same paper that of moving media.
In the next paper on this subject ^ the correct principle of the continuity
of the stress normal to the bounding surface is introduced in place of one
of the other conditions, but it is supposed that the term involving the
dilatation disappears in consequence of the incompressibility of the ether ;
in reality, as Green showed, the coefficient of that term is very large, and
it must be retained to give correct results. Ketteler fails to see this, and
hence concludes that the retention of Green's longitudinal wave is
unnecessary. He then considers, as Green had done, the problem of total
reflexion ; and, through not taking into account the continuity of the dis
placement normal to the surface, appears to be able to do without the
longitudinal waves. The motion of the matter particles does not come
into consideration.
Another series of surface conditions are given in the next paper on the
subject,'* and the matter particles being treated merely as a sort of
' Ketteler, ' Beitrage zur einer endgiiltigen Festst^Uung der Schwingungsebene
des polarisirten Lichtes,' Wied. Ann. t. i. p. 206.
' Ketteler, Wied. Ann. t. i. p. 5.56.
' Ketteler, ' Zur Theorie der longitudinalen elliptisclien Schwingnngcn im incom
pressiblen Ether,' Wied. Ann. t. iii. pp. 83, 284. See also Theoretisclie Optili, p. 130.
•• Ketteler, ' Ueber den Uebergang des Lichtes zwisclien absorbirenden isotropen
nnd anisotropen Mitteln und iiber die Mecbanik der Scbwingungen in denselben,'
Wied. Ann. t. vii. p. 107.
ON OPTICAL THEOEIES. 239
ballast, their motions do not come into the surface conditions. "While,
finally,' Ketteler adopts the principle enunciated by Kirchhoff,^ and
already discnssed above,^ viz. that no work is done by the action of the
stresses in the media on the bounding surface. In applying this principle
he equates to zero, as Kirchhoff has done, the terms involving the dilata
tion ; and this, as has been already shovs^n, leads to MacCullagh's formulae
on his assumption as to the equality of the density in the two media, and
to Fresnel's if the rigidity be assumed equal in the two. The theory is
applied to metallic reflexion and total reflexion within crystals in another
paper.^ Thus, while Ketteler's first theory ^ was in reality Green's
erroneously altered, this second theory is that given by Kirchhoff" in the
paper ah'eady quoted. Neither of them really seems to me to involve the
distinctive features of Ketteler's theory of the propagation of light.
§ 2. Voigt's theory is contained in the paper already referred to.^
The conditions assumed are : —
I. The displacement of the parallel to the surface ether is continuous
in the two media.
II. The displacement normal to the surface multiplied by the density
is continuous.^
III. Kirchhoff"s principle — viz. that the work done by the stresses on
the interface of the two media vanishes.
In evaluating the expression for this work Voigt takes into account
correctly the terms arising from the action of the matter on the ether.
The displacements which come into the equations expressing the first
two conditions are strictly displacements of the ether relatively to the
matter, but since it is assumed that the motion of the matter particles
is very small compared with that of the ether, the absolute displacements
of the ether particles are introduced.
The results arrived at, however, are hardly satisfactory. In the first
place, in evaluating the expression for the work done on the surface, the
term involving the dilatation is omitted. Voigt has taken it into account
in his equations of motion ; his reason for omitting it here is not given.
He thus avoids the question of the socalled longitudinal vibrations.
_He then considers the case of vibrations at right angles to the plane
of incidence, and arrives at the formulae —
E, + R, = D. .
(^1 4 r,  ni !2) (E,  R,) sin^j cos^i ■ . . (74)
= (wi2 t r.j — «2''^) Dj8in02cos^2 ■
B, R, and D being the amplitudes of the incident reflected and refracted
waves.
' ' Ketteler, ' Optische Controversen II.' Wied. Ann. t. xviii p 632
'' Kirchhoff, Ahhandl. der Berl. Ahad. 1876, p. 57.
' See p. 193.
* Ketteler, ' Ueber Problems welche die Neumann'sche Eeflexionstheorie nicht
losen zu konnen scheint,' Wied. Ann. t. xxii. p. 204.
' See p. 162.
« Voigt, ' Theorie des Lichtes fur vollkomnien durchsichtige Median,' Wied. Aim.
t. XIX. p. 873. See also Voigt, ' Ueber die Grundgleicbungen der optischen Theorie des
Merrn E. Ketteler,' Wied. Aim. t. six. p. 691, especially p. 696 sen.
' See p. 186 ; also Cornu, Ann. de Chim. (4), t. xi. p. 283.
240 EEPOKT— 1885.
These become MacCullagh's and Neumann's formulas on the assumption
that
???, +ri = ?Ho + r, )
  . . . . (75)
They become Fresnel's if
' ... (76}
' I
a\=a
for these equations lead — remembering the value of the velocity — to the
condition —
m^ + ^1 — WjT^ _ sin 2^ 2
m^ + r^ — ^2^^ sin^0,
For the vibrations in the plane of incidence the results of the first and
second principles are inconsistent with that of the third. For the first
and second give
(E„ + R^) cos^i = DpCos^)2 )
771 1 (E^ — R,,) sin ^ 1 = mj D,, sin ^2 >
while the first and third give, instead of this second equation,
(to, + r, — H., r^) (Ep — Up) sin*! = (wg + ?'2 — "2'') Dp sin02 • (78)
They become consistent If Ave assume mi ^7^21 ^^d, adopting Neu
mann's hypothesis,
r, = r2. Ml ="2,
or, adopting Fresnel's,
ei+ai = e2 + a2) ci''i=ct'2
In another paper' it is shown that KirchhoflT's principle, when applied
to circularly polarising media, leads to an impossible result, and the
principle is modified by the supposition that the work done is a function
of the time only, and not zero.
The theory of ordinary absorbing media is developed ^ from the
supposition that terms involving a loss of energy may come in through
the mutual reaction of the ether and matter, and it is shown that these
would lead to terms of the form — t —  + cv^, in the equation for
at at
u, which merely becomes, for waves travelling parallel to z,
where
(80)
In considering the problem of reflexion in this case, Voigt assumes
that the plane xy being the face of incidence, Mtw is continuous. The
' Voigt, ' Das G. KirchhoflE'sche Princip und die Tlieorie der Reflexion und
Brechiing an der Grenze circularpolarisender Medien,' Wied. Ann. t. xx. p. 522.
^ Voigt, ' Theorie der absorbirenden isotropen Medien,' Wied. Ann. t. xxiii. p. 104.
M.
dH
dt^
= A,
dho
—
,du
^d!
+ '
^dzm
M.=
:«l,
+
'"i 
"•1
r
A,=
= e,
4
«i 
a',
72
f
]
ON OPTICAL THEORIES. 241
principle laid down in the former paper ' would require that this should
be mw, not Mw, as he points out, remarking that the equation given is only
true under certain restrictions, and, in fact, he shows that for vibrations
in the plane of incidence the continuity of Mw is inconsistent with the
energy equation, at least unless & = 0. The energy equation gives
M.,w,=^L,w._h^T^ I . . . (81)
and this form is assumed for the rest of the work.
Expressions are then found for the difference of phase between the
reflected, refracted, and incident beams, and for their relative intensities,
and these are compared with theory on the assumption that the con'
stant h vanishes, and that Mj =M2. The results of the comparison are
satisfactory; but this, however, can hardly be said for the principles
from which they are deduced, while the difficulties we have already
alluded to as to the negative value for the real part of the square of the
refractive index remain in their full force.
Chapter IV. — Theoet of Sir "William Thomson.
General Considerations.
§ 1. The lectures of Sir William Thomson delivered last year at
Baltimore have developed a new interest in the theories now under con
sideration. After discussing at some length the elastic solid theory and
throwing much light on it, and on the meaning of the twentyone
coefficients of Green's theory, he points out its unfitness to explain the
phenomena, and then proceeds to work out the consequences of a special
form of reaction between the ether and matter ; this he illustrates in his
own inimitable manner by his mechanical model of the ether within
a transparent body. This mechanical model consists of a number of
concentric hollow spheres. Each sphere is connected with the one
withm it by zigzag springs, and in the centre there is a solid mass
connected also by springs with the shell next to it. The dimensions of
these shells, which represent the matter molecules, are supposed to be
small compared with the wave length. The interior molecule will have
anumber of periods of vibration depending on the number and nature
of the spring connections, on its own mass, and on the masses of the
shells. The springs are supposed to be massless. The shell molecules are
distributed through the ether in very large numbers, and the outermost
shell is connected with the ether.
It is further supposed that the forces arising from the springs are
proportional to the relative displacements of the centres of the shells, and
that the ether acts on the first shell with a force proportional to the
relative displacement of that shell and the ether surrounding it, so that, if
4 be the ether displacement, .^,, Xo those of the shells, mJ4,7r'\ m^/47r^, etc.
their masses, the equations of motion are,
m.
4^2 ^ = <^2 (2^1  aJa)  C3 i^i  X3)
' Voigt, Wied. Ann. t. six. p. 900. See above, p. 239.
looo.
(82)
E
242 EEPOET— 1885.
etc. If we suppose the whole motion to be harmonic and of period t, then
the equations become
^f^i = G,{i,x^)C^{x,x^) . . . (83)
etc., from which the motion of the various shells can be determined.
The system will represent Helmholtz's theory if we suppose the viscous
terms in his expression to vanish, and consider only a single shell. The
solution in the general case is carried further by putting
and ^^._ _ C,x,,
The equations may then be written —
u
• (84)
Wj = tti
«2 = ^2 — ^'^
(85)
"s /
etc., whence we find Mj as a continued fraction.
By differentiating these expressions with reference to t~^, and writing
^ for , we find —
Su, = 7», + (9i±l ] w .^ , + (^i±&A \^^ + , etc. . . (86)
Hence
J^'=73^7{^^^.^ + .>.^>l+ • • • •} . . (87)
Thus tt decreases as r increases, and if we start from r, a small quan
tity, the us are all large and positive ; hence alternate shells are movincr
in opposite directions, and the motion of consecutive shells rapidly
decreases.
As r increases the ii's decrease, and after a time one will become
negative, passing through zero — it can be shown that ttj is the first oije
thus to become negative. This gives the first critical case in the solution,
for then re, is infinitely great compared with ^, and the solution fails.
This equation can be put into the following more convenient form —
.^=li{jM^+Ji!^ + . ...}.. (88)
where c,, (C2, etc., are the critical values of r, and R,, Rg, etc., represent
the ratio of the energy of the several shells to the whole energy of the
system.
To apply this to the motion of the ether in a transparent body, let
«ii/47r2, etc., represent the whole mass contained within shell No. 1 per
unit vol., let p/47r2 be the density, and el^v"^ the rigidity of the ether, aud
suppose the first shell, of mass m,, to be connected by a spring to a massless
ON OPTICAL THEORIES. 243
spherical lining, which is in rigid connection with the ether outside.
Then the equation of motion is —
Let the solution of this represent a train of waves of period r and
length X, and let V be the wave velocity for the medium. Then
and if n be the refractive index, since the velocity in free space is y/ ejfj
we have, if we put Ciki^Ri=g',mi, etc.
P L
+ gi^i^ fe + TT +••••) ~ *®^™^ ^^22, ?3 I . • (91)
It follows from this that, ji must be very little less than unity if the
formula, neglecting the terms in q^, etc., is to apply to a transparent sub
stance such as rock salt, which gives a value for^ between 1 and 2 for
a range of the spectrum from the visible light to the longest waves emitted
by a Leslie cube. The formula, we note, is the same in form as that
given by Ketteler and Biuot (see above, page 181), and Ketteler has
shown that in some fairly transparent substances the coefficient 1 — ^i is
appreciable, gi ^s essentially less than unity, so that the term in r^ comes
in with a negative coefficient. The formula, then, will explain ordinary
■dispersion fairly if we put q2, 23) ^tc., all zero and take r greater than ki.
The critical cases are then discussed from the form
In this, r is greater than k\ and less than /cj for ordinary refraction.
As r decreases down to k^, jj? passes through the value infinity and then
becomes negative, we have greater and greater refraction, and then the
waves cease to be transmitted and absorption takes place.
And here we are met with the question — What becomes of the energy
thus absorbed ? According to our equation the ratio a;, jl becomes infinite,
and the solution as it stands fails to meet this difficulty. Helmholtz
introduced the term —y'^dJJIdt into the motion of the first shell, and this,
representing as it does a viscous consumption of energy by the matter
rnolecules, is objected to by Sir Wm. Thomson. Helmholtz's solution
given on p. 221 becomes identical with that at present under discussion if
we put y=0 ; it is to meet this case in which t^c, that the term in y* is
introduced, for if k represent the coefficient of absorption on Helmholtz's
theory, and we suppose y to be small, then, with Thomson's notation,
•v2t<
(t*  Ki2)»
very approximately, K being a constant, and Jc may be very small except
when r is nearly equal to k^.
B2
h'
244 EEPOET — 1885.
In order to acconnt for the extreme transparency of a substance such
as water, we must suppose h to be so exceedingly small that Sir
William prefers to consider it as zero, and says : ' I believe that the first
effect when light begins, of period exactly equal to c,, is that each
sequence of waves throws in some energy into the molecule. That goes
on until somehow or other the molecule gets uneasy. It takes m,
(owing to its gieat density relative to the ether) an enormous quantity
of energy before it gets particularly uneasy. It then moves about, and
beoins to collide with its neighbours, perhaps, and will therefore give you
heat in the gas if it be a gaseous molecule. It goes on colliding with
other molecules, and in that way imparting its energy to them. This
energy is carried away (as heat) by convection, perhaps. Each molecule
set to vibrating in that way becomes a source of light, and we may thus
explain the radiation of heat from the molecule after it has been got intO'
it by sequences of waves of light.'
Helmholtz's equations are, of course, the more general, and apply to
an absorption band as well as to the part of the spectrum for which the
medium is transparent. It would seem that the term —y^dU/dt may
rightly represent just the effect of that loss of energy in the form of
heat due to the irregular collisions of which Sir William speaks, an
effect which is only appreciable in the result when, owing to the
coincidence of the periods, U tends to become large compared with u, or,,
in Thomson's notation, Xi large compared with ^, and in this case x^ will
not become infinite, for the amplitude will be multiplied by the factor
e*^', and k being large, the limit of the product comes into consideration.
Such a system oF ether with attached matter molecules is thus shown
to account for the phenomena of dispersion. A serious difficulty, how
ever, is encountered when we reach the problem of double refraction.
§2. For we may suppose, in order to account for it, that C, is a func
tion of the direction, and that for two principal directions it has the
values Ci and C/, while C2 is a constant independent of the direction.
Then, with only one enclosed mass,
h  Co)
,, = l + C^All ±, .... (93)
and to give a dispersion formula resembling Cauchy's we must have
7Hi/2 considerable compared with C2,_and Ci large compared with either.
Hence, if /i' be a second principal index,
//2=1 +
C
and therefore r'^fc — — ^
p (c, + c,^')(c/ + c.5)
which, remembering the relative magnitudes of the quantities, and writ
ing Dand D' for the approximate values of the denominators, becomes
ON OPTICAL THEOKIES. 245
60 that the difference between the squares of the refractive indices will
be inversely proportional to the squares of the wave length, and this is
quite contrary to experiment. The question as to whether the theory
here suggested would lead to Fresnel's construction is not considered.
In a later lecture Sir "William returns again to the question of what
becomes of the energy absorbed by the molecules, and of the nature of
the ether. As to the latter he adopts Stokes's view, that the medium may
be perfectly elastic for the small disturbances of a lightwave, executed,
as they are, in the twentymillionmillionth of a second, and yet be a
perfect fluid in respect of forces which act, as may be supposed in the
kinetic theory of gases, for the onemillionth of a second. Now, the
numerical calculations of Professor Morley, undertaken at Sir William's
suggestion, show that the energy given to a system such as described
tends to become absorbed by the vibrations of lower modes, so that the
original energy appears as vibrations in which the period may be the
millionth of a second instead of, perhaps, the twentymillionmillionth, and
this energy shows itself in the motions which we deal with in the kinetic
theory of gases, rapid it may be in themselves, but slow compared with
the light vibrations.
§ 3. Metallic reflexion and the quasimetallic reflexion of such sub
stances as give anomalous dispersion are dealt with, and it is shown that
the phenomena are such as would be produced by making jx^, a negative
quantity, and this is given by values of r a little below the critical period.
Thus the molecular explaaation of the great reflecting power of silver
is that the highest mode of vibration of the molecules with which silver
loads the ether is graver than the mode of the gravest light or radiant
heat which has ever been reflected from silver ; and if, again, for certain
modes /x^ is not negative, but less than unity, it shows that, conformably
with the experiments of Quincke on gold leaves, we should expect light
to travel through the medium faster than through air. This forms a
marked and most important distinction between this theory and others
which have been given to explain metallic reflexion. For the other
theories the metallic effects arise from the importance of the viscous
terms of the form —ydujdt.
In an appendix Sir William works out the problem of reflexion and re
fraction, following Green and Lord Rayleigh so far as ordinary transparent
media are concerned. He then transforms Green's formute for vibra
tions in the plane of incidence to the case in which /x^ is a real negative
quantity, and arrives at formula expressing, on a strict elastic solid
theory, the intensity and change of phase in a wave reflected from metal.
According to this solution we have, if v"^ = — fx^ so that v^ is positive,
the values of * and ^ given by —
* = — >'^ cos (aa!&y + w<) + tan fl!^^*— ^tL_i_ sin {ax + 1]! + ut)
*i= — v^cos{ax + hy + ut)—\ja.nd ^^'''^ ' sin ( + aa.' + &y + wQ
r^ — 1
. vVj'2 + 1^ , . , \. (95)
^ =  ^^ _^' e"^ sin (by + wt) 1 ^ '
*' = _ ('' + !)
v'l
bx
sin (ly + ut)
246 REPORT— 1885.
These are simplified if we put —
A2 = ((,.2 + 1) 52 + ,,2^2} r^ + tan B Q^^t^l , 2 = tan/
S = v^ sec/
(96)
and the displacements in the transparent medium are then, for the incident
wave,
and for the reflected.
— — S sin (ax + hy + wt +/),
A
— S sin (— ax + ly {■ wt — /).
A
In this case the rigidities in the two media are supposed to be equal.
Sir William has also worked out the problem in the case in which the
rigidities are not equal, in the hopes that by this assumption combined
with variations in the density — or rather effective density — the variations
from Green's formula in the case of light polarised at right angles to the
plane of incidence may be accounted for. He finds, however, that,
any difference of rigidity which might, combined with a difference of'
density, be sufficient to reconcile Green's theory with experiment would
cause the proportion of light reflected at normal incidence to be greater
than {(/u — l)/(/j + 1)}2, and this value, given by Green's theory,
agrees closely with Rood's experiments. We are thus driven back to
Lord Rayleigh's case of equal rigidities in the two media. For metals,
then, we are to have the rigidities equal, and the value of ^i^ decreasing'
from — 00 when r = /.i to zero when r = /., /N, N being some laige nume
rical quantity, and then again augmenting from zero to unity as r
decreases from kJ'N to 0. ■
The dynamics give no foundation to a theory such as Cauchy's, in
which n' is a complex quantity. For light polarised in the plane of inci
dence we have, if n and n be the rigidities, and
r = n'/n, )
... (97)
and tan e = i(i sec^^^ + tan^ej^j
R = i (H r2(v2sec2 I tan^e)} ^
4 = R cos {ax + by+o)t — e) i . . . (98)
^= R cos (— ax + by + wt + e) )
for the incident and reflected wave ; and for the refracted wave,
f = /T^(^ + ^"'=«^cos(%FwO . . . (99)
According to these formulaj the reflexion is total from a metal surface at
all angles of incidence. Sir John Conroy has recently shown that the
loss is exceedingly small. If light be polarised in any plane, then the
vibration in the plane of incidence is retarded relatively to that at right
angles to that plane by the amount 2f+ 2e — tt. If we suppose v and rv
to be both very large numerics, this retardation becomes —
ON OPTICAL THEORIES. 247
and from the observations wliicli have been made on the value of the
principal incidence, for which the retardation is ^tt, we can find a value
for rr. For silver Sir J. Conroy's observations give (rv)~^ = 3'65.
And here we are met with a great difficulty. Experiments show that
there is very little chromatic eflPect about metallic reflexion. Thus, since
the value of the principal incidence depends mainly on ry, this quantity must
be independent of the period. Now v^ + 1 is approximately proportional
to T^ when r is small compared with Ki, and so this result requires that r,
which is proportional to the effective rigidity, should also vary in a certain
definite manner, and it is difficult to see how the theory is to give this.
The theory is then applied to the case of a thin metal plate, and leads
to the fact that the phase of both components is accelerated by the
transmission. The accelerations for the two cases are given by —
c cos ^+( — — — l^^, vibrations normal to the plane of incidence,
d cos 9 + ( T~ — ) \ vibrations in the plane of incidence,
V4 Try
when S is the thickness of the plate, and e and /are found in the same
manner as above.
This acceleration was discovered by Quincke, but the details of his
results do not agree well with the formulas. The formulas are consistent
with Kerr's discovery of the rotation of the plane of polarisation by
reflexion from an iron plate when magnetised, but not with Kundt's
result that transmission through a thin plate of iron in a magnetic field
produces a very large rotation of the plane of polarisation.
In a final appendix an account is given of a gyrostatic molecule, the
properties of which would give to the medium the heliacal effects seen in
sugar and other active solutions. The molecule consists of a spherical
shell in which are imbedded two gyrostats having a common axis, which
initially is a diameter of the shell. One end of each axis is connected
with the shell by a ballandsocket joint, while the second extremities of
each are connected together at the centre of the shell by a second ball
andsocket joint.
§ 4. Having thus given an account of the various theories proposed
based in some way on the mutual reaction between th,e ether and matter,
it remains to compare and contrast them.
The theories of Boussinesq and Voigt have much in common, and
neither of the two as they stand applies to the case of bodies showing
strong absorption, for the matter motion is entirely neglected. The theo
ries of Sellmeyer, Helmholtz, and Thomson come under one head in
that they all make the mutual reaction to depend on the relative dis
placement of the matter and ether.
Lommel's theory seems to me untenable : in its original form it con
tradicts the third law of motion, and if modified so as to be consistent
with that, it leads to impossible laws for the relation between refraction
and absorption ; besides this, his theory of double refraction does not
lead to Fresnel's wave surface, and there seems no reason why the co
efficient a^, which occurs only in the equation of motion of the matter,
should be the one to be treated as a function of the direction. The laws of
circular polarisation and of the double refraction in quartz, to which the
theory leads, and which seem to agree with experiment, may be obtained
248
EEPOKT 1885.
with sufficient approximation to fit the experiments from other theories ;
and, indeed, the fact that the wave surface in quartz does not become a
sphere and a spheroid when the heliacal terms are neglected is fatal.
"With regard to Ketteler's theory in the form finally given to it by its
author,' it seems to me to have no possible mechanical basis. With the
interpretation which he gives of the constants involved, his equations
appear to contradict Newton's third law as effectually as do Lommel's,
while, so far as the problem of reflexion and refraction is concerned, I
cannot recognise the validity of Kirchho0"'s principle as it is applied by
Ketteler. At the same time I think that the suggestion of Ketteler — to
which, however, he himself takes objection— already mentioned, leads
to results which, so far as dispersion is concerned, agree closely with
experiment.
We may with advantage compare the dispersion formula which it
gives with that which comes from the theories of Helmholtz and Thomson.
If we neglect the terms depending on viscous action, we have, accord
ing to Helmholtz, for ^, the refractive index,
( \* ^
:1
pXi
f""i
^1^
^1
(100)
while, according to the modified form of Ketteler,
f °
5 '■
1 + S U2
1— 
(101)
Ketteler's equations come from Thomson's or Helmholtz's by writing
for C, the quantity — 4^20, /r^, or for /j^ in Helmholtz's notation — n^pi^.
We may write Ketteler's equation in the form of a series thus —
=^l [l+lD{*f + j^;*+ ....}] . (102)
two terms of which will give us Cauchy's series with three constants.
This modification leads also to an escape from one of the difficulties
suggested by Sir William as to the explanation of double refraction.
For his general expression for yu^ will become, if we write for Cj the
value 4T2Ci/r2,
47r2C,
yu2 = l +
+
•)}
(103)
If we neglect for a moment the terms on which the dispersion depends,
as being small compaied with the term 4Tr^Cilp, which gives rise in the
first instance to refraction, we get that
4^r2(CjC/)
(104)
and there will be double refraction independently of the period.
' Ketteler, ' Zur Dispersionstheorie des Lichtes,' Wied. Ann. t. xxi. p. 199.
ON OPTICAL THEORIES. 249
It is another question, and one which we shall discuss shortly, whether
the double refraction thus produced will give rise to Fresnel's wave surface.
There seem, then, to be reasons why we should expect terms such as
Ketteler has suggested in our equations — terms which will make the mutual
reaction of the ether and the first matter shell depend rather upon their
relative accelerations than upon their relative displacements. It is not so
€asy to suggest a mechanical connection between the ether and matter
which would give rise to this force, but at the same time there is, I
think, no mechanical reason to be urged against it.
Voigt's theory of wave propagation is in one way more comprehensive
than those we have considered, while in another it is less so. It is more
romprehensive in that it includes both sets of terms with some others in
the expression for the mutual reaction ; it is leas so in that it treats the
ratio U/m as a small quantity which may be neglected. This same
remark applies to Boussinesq, whose work in one sense is more general
that Voigt's, in that he considers the efifect of the attached molecules on
the condensational or pressural wave.
The presence of these molecules has been shown in Bonssinesq's
paper to alter the effective compressibility of the medium as well as its
density and its rigidity. In the ether we assume that the compressibility
is small compared with the rigidity, so small that the ratio of the two
may be neglected, and this must still be the case, even when the ether is
loaded. But when dealing with the problem of reflexion we are concerned
with the refractive index of the medium for the condensational wave.
This will depend on the ratio of the two effective compressibilities, as
well as on that of the two effective densities, and though either of the
two compressibilities may vanish when compared with the rigidities, in
considering their ratio it becomes necessary to take into account any
change due to the loading of the ether.
It may not be unreasonable, then, to suppose that the effective density
of the ether for the condensational wave is different from the effective
density for the transverse wave. This supposition would account easily
for the variation from Green's formula observed when plane polarised
light polarised at right angles to the plane of incidence is reflected from
a transparent surface, in that it would allow us to introduce the second
constant jjq, as suggested by Haughton and Lord Rayleigh.'
Let us now consider Voigt's theory. With regard to the problem of
reflexion his surface conditions appear to be unsound. The ether is the
continuous medium, and the surface conditions must apply to it simply.
The conditions of continuity demand that the actual displacements of the
ether and the actual stresses over the interface, arising, of course, in part
from the action of the matter, should be the same in the two media.
The validity of Kirchhoff's principle has already been considered, and it
has been shown that it does not lead to results in accordance with experi
ment, for it does not give the change of phase which in some cases
accompanies reflexion.
But, while this is so, Voigt's theory shows us that the effects of the
attached molecules may show themselves either in the rigidity or the
•density of the ether. Now, the work of Lord Rayleigh and Lorenz has
proved that the effects of reflexion are due mainly, if not entirely, to
differences of effective density ; and so we must look to the terms in
' See p. 192.
250 BEPOET — 1885.
Voigt's theory whicli aflPect the density as the most important. These
terms are
_(,g,+ „)(„U).
The other terms,
show themselves as a variation of the effective rigidity. In order to
obtain a consistent theory of reflexion we must treat these as of secondary
importance compared with the first terms. Now, this is inconsistent with
both theories of double refiaction as advanced by Voigt, for the first
condition for either is that r and n must be independent of the direction.
It would seem from this that they should be the same in all media.
Boussinesq adopts the opposite view. He makes his double refraction
depend on the terms which correspond to r and n, and neglects the
variations of the others with the direction. If we do this — and we seem
to be forced into it by the further requirements of our theory — the funda
mental equations in a crystal become those given by Lord Rayleigh.
These, we have seen, if we assume the strict transversality of the
vibrations, do not lead to Fresnel's wave surface. On the other hand, if
we suppose that the vibrations in a crystal are at right angles to the
ray, not to the wave normal, the result agrees with all the consequences
of experiment, for we obtain Fresnel's surface as the wave surface, but
we are left in a difficulty as to the normal wave.
With regard to metallic reflexion, the theory as given by Sir "W.
Thomson explains completely the difficulty raised by Lord Rayleigh as to
a negative value for ^^. It does not, however, enable us to decide how
much of the effect is due to the fact that the highest possible free period of
the ether in the metallic medium is below that of the incident light, and
how much is due to opacity arising from terms such as dujdty&s supposed
by Lord Rayleigh. The correct equations to which such a theory would
give rise are yet unsolved, but the principles required by the solution are
well known.
It seems, then, that this theory promises to afford us the solution of
the difficulties which still surround theoretical optics, and to account at
once for the phenomena of reflexion and refraction, dispersion and double
refraction. Of course, in all cases of transparency the matter motion is
infinitesimally small compared with that of the ether. The ether is to
be looked upon as moving through a sort of network of fixed matter
particles. Terms depending on the reaction between the ether and
these fixed portions of matter will be introduced into the equations,
and these terms will be expressible as functions of u, v, w and their
differential coefficients. The matter particles will not move appreciably,
and their movement is not necessary for the explanation of refraction and
ordinary dispersion ; for on Ketteler's modified theory we have, if we
omit the viscous terms,
in rrifx (»'''* — «,*)'
and the ratio of the amplitudes is
/32n2
fi(^v'^ — n'^)
ON OPTICAL THEORIES. 251
From the value of /i^ we see that y3^ must be comparable with m, the
density of the ether, so that, except when «^/(»2 — ?t^) is a large
quantity, the ratio of the amplitudes will be inversely as the densities, for
l^^/fj will be comparable with mjij. When, however, nj{_v^ — ii^) is
large, the matter motion becomes appreciable, and the phenomena of
anomalous dispersion arise.
Part IV.
THE ELECTROMAGNETIC THEORY.
Chapter I. — Maxwell's Theory.
§ 1. There remains now for consideration Maxwell's electromagnetic
theory. The fundamental equations of this theory are purely electrical,
and are established on electrical principles. According to Maxwell, when
electromotive force acts on a dielectric medium the change of condition
known as electric displacement is produced. The two are connected by
the equations —
P = ^/, etc (1)
P, Q, R being the components of the E.M.F. and /, g, h of the dis
placement. K is the inductive capacity. In a crystal the equation
holds only for the principal axes, and along these K has three diiferent
values.
The rate of variation of the displacement given by/, g, h constitutes
the current in the medium, and it is an essential part of the theory
that —
df do dh
— + — +
d.e dy dz
vanishes everywhere.
The current is connected with the components of the magnetic in
duction a, b, c by the equations —
de dh . J ._,
etc., and the magnetic force a, /3, y is given by
a = fici (3)
etc., where /i is the coefiBcient of magnetic capacity.
a, b, c are also given in terms of a quantity known as the vector
potential, the components of which are F, G. H, by the equations —
fZH dG
''=dy~^ ^^^
etc., and from these it follows that
W=^V2F .... (5)
etc., where
j_ dF ^ dB.
dx dij dz
252 EEPOET — 1885.
while the electromotive force at any point is also determined in terms of
this same quantity F, G, H by the equations
p_ dF d^ ,
etc., ^[' being the electrostatic potential. From this it follows that
,K^(^+f)v^F+.f=0 .... (7)
dt \ dt dx J ax
etc., and the vector F travels through the medium with velocity 1/n/K^.
Now, the value of this quantity can be determined by experiment, and
agrees very closely indeed with the velocity of light. Thus the vector
potential, and in the same way the electric displacement and the magnetic
induction, travel through the medium with a velocity, as nearly as we can
eay, identical with that of light.
Moreover, the electric displacement corresponding to this is in the wave
front, and the same is the case with the magnetic induction a, h, c. By
this motion energy is conveyed through the medium, the electrostatic
energy depending on the electric displacement, the electrokinetic on the
magnetic induction, and the two can be shown to be equal. Thus the
theory agrees with the undulatory theory of light in assuming the exist
ence of a medium capable of becoming a receptacle of two forms of
energy. Electric displacement and magnetic induction are, then, changes
of condition which can be propagated in waves of transverse disturb
ances through the medium with a velocity practically identical with that
of light. Maxwell's theory supposes that there is an intimate connection
between the vibrations which constitute light and electric displacement ;
according to some of his followers the two are identical, though, so far
as I can judge, that is not necessary to the theory as he left it.
Now, experiment shows that the value of /j. is nearly the same for all
media, so that it follows that on this theory the specific inductive capa
city of a medium — the ratio of its inductive capacity to that of air —
should be equal to the square of the refractive index. Experiments have
shown that while this law is by no means true for all substances, it is suffi
ciently nearly so for many to render it probable that V K gives the most
important term of the index.
In estimating the value of the comparisons we must remember that
while K is determined by observations lasting over an appreciable time,
the refractive index depends on vibrations of great frequency ; to compare
the two, then, we have to adopt some dispersion formula, and find the
value of the index for waves of infinite period, and this alone is a source
of error.
Again, the equations for a crystalline medium are obtained by Maxwell,
and he shows that the velocity of wave propagation is given by Fresnel's
construction, while the electric displacement is in the wave front, and its
direction is that of the axis of the ellipse which determines the velocity.
The theory is not burdened with a wave of normal vibrations, and
accounts quite simply for all the phenomena of double refraction.
§ 2. The theory of reflexion and refraction of electromagnetic waves
was first given by H. A. Lorentz,' who follows a method of attacking the
' Lorentz, SMomilch. Zeitschrift, t. xxii.
ON OPTICAL THEOEIES. 253
problem which is dae to Helmholfcz.' This we shall consider later. It was
also solved by J. J. Thomson,^ so far as the isotropic media are concerned,
and by Fitzgerald. ^
Some further developments of the theory are given in a paper by the
author of this report, and read before the Cambridge Philosophical
Society.*
In this paper the general equations for the displacement and for the
magnetic induction in a crystal are given. If a, b, c be the principal
velocities given by the equation
2 1
3tc., then
dt^ •' dx\ dx dy dz J ^ '
etc., while
d'^n, J (i^a TO d^a ^ d^a
— i. ("a"^" +62^+0^^^ . . . (9)
dx\dx dy dz ) '
If a wave of electric displacement S', in a direction in which the
inductive capacity is K', be traversing the medium, the electromotive
force is 4!7rS'/K' in the direction of displacement, and 4rrS' tan x/^'
along the wave normal, when x is the angle between the ray and the
wave normal.
§ 3. The surface conditions implied by the theory, and used by Lorentz,
J. J. Thomson, Fitzgerald, and Glazebrook, are that the electric and
magnetic displacements normal to the interface are continuous, while the
electric and magnetic forces in the interface are also continuous.
The formulae obtained are identical with those given by MacCuUagh
and Neumann, electric displacement being substituted for the ordinary
displacement of the medium.
The theory has the very great advantage over the ordinary elastic
solid theory that reflexion and double refraction are both explained by
variations in the same property of the medium, viz. the inductive capacity.
Variations in its value from medium to medium give rise to reflexion and
refraction ; variations in different directions within the same medium are
the cause of double refraction.
§ 4. The theory has been applied by Lord Rayleigh to account for the
various phenomena ^ connected with the scattering of light by a cloud of
small particles. These are deduced satisfactorily from the theory on the
supposition that \i, the magnetic capacity, is a constant through the two
media, and that the effects are due to variations in the inductive capacity,
while, when terms of the second order in A K/K are included, the scattered
light does not vanish — the incident light being plane polarised — in a direc
' Helmholtz, Sorchardfs Journal, Band Ixxii.
"^ J. J. Thomson, Phil. Mag. April, 1880.
» Fitzgerald, Phil. Trans. 1881.
■• Glazebrook, Proc. Camh. Phil. Soc. vol. iv. p. 155.
' Lord Rayleigh, ' On the Electromagnetic Theory of Light,' Phil. Mag. Aug, 1881.
254 EEPORT — 1885.
tion normal to the incident light, but in one inclined at an obtuse angle
to that in which the light is travelling. Tyndall observed this effect
when the particles scattering the light cease to be very small.
Chapter II. — Hei.mholtz's Theory.
§ 1. Helmholtz looks at the problem of the propagation of an
electromacrnetic disturbance in a somewhat different manner, and a com
parison of the two theories is given by the author of this Report.' 
The electromagnetic effects in the medium depend, according to I
Maxwell, on the values of F, G, H, the components of the vector potential, 
or as Maxwell also calls it, of the electrokinetic momentum, and if
we integrate round a closed curve, the values of F, G, H satisfy the
equation
[Fdx + GdyB.dz = {{'^ dsda . . . (10)
where ds is an element of the curve, i the current at any point at a
distance r from ds, da an element of the curve in which the current i is
running, £ the angle between (7s and da, and the integration on the right
extends round the two carves s and a.
From this we can show that
And if we put
we find that
4fli
dx'dy'dz' +^
dx
4^ + ^+^'=lv2*
dx dij dz 4
V 2F — —  = — 47r/i/ + fi
dx dxdt
lb
r ^dF ^db ,dB. M
Helmholtz, starting from the equation
f Ydx + Gdy + B.dz = ff '""^' ds da,
invest! gates^the most general form which F, G, H can have. He shows
that we must write for  ^ of equation (11) the value
Ml^*^,"'' • • • (">
where fc is an unknown constant. Hence
v'F = W+.(l'O0, . . . (W)
and by comparing this with (13) we see that
3=Hk^ (16)
dt
' Glazebrook, Proc. Camh. PhU. Soc. vol. vi. pt. ii. See also J. J. Thomson,
■' Report on Electrical Theories ' p. 133 oE this volume.
ON OPTICAL THEORIES. 255
If it be necessary that J should vanish, then Z; or — mnst be zero.
dt
According to Helmholfcz, however, J is not necessarily zero, and the
equation to determine it is —
^&kJ=a^J (17)
so that J, and therefore *, is propagated through the medium as a
wave of normal disturbance with the velocity
1
«uK
On Helmholtz's theory there may therefore be a normal wave in addition to
the transverse wave. Helmholtz's theory becomes Maxwell's if we put
* = 0, and then unless the value Z; = oo is admissible J = 0, and there
is no normal wave. If Z; = there will still be no normal wave for its
velocity will be infinite.
When we consider the problem of double refraction, we can show that
all the possible directions of vibration L, M, N corresponding to a given
wave normal I, m, n are given by the equation —
■ E (^'  ^' + M ('" '^') + I ^^" ^') = • • (IS)
There are therefore, in general, an infinite number of such directions.
If, however, we are to assume that there are only two, and those the two
given by Fresnel's theory, we must have IL + wiM + nTS = 0. Thus
Maxwell's solenoidal condition,
^+'ll+f=Q .... (]9)
ax dy dz ^ '
is a necessary and sufficient condition to give Fresnel's construction.
Chapter III. — Dispersion, etc.
According to the theory as left by Maxwell, waves of all lengths
travel at the same rate. Dispersion does not come into consideration.
This question has been dealt with by Willard Gibbs • and H. A. Lorentz.^
§ 1. According to Gibbs's views the displacements of which we are
cognisant in the phenomena of light are the average displacements taken
through a space which is small in comparison with the wave length, but
contains many molecules of the body. The real displacement at each
point of such an elementary space probably differs considerably from the
average value, and a complete theory should take into account the two.
This is done in Gibbs's paper The average displacements being I, r), ^,
the complete displacement is taken as ^ + ^', &c. I', r,', ^' are denoted' as
the irregular parts of the displacements. It is shown that i\ r]', C are
linear functions of ^, 77, i; ; they are therefore of the same period, and the
phase of the irregular displacement throughout the element Dv is the
' J. W. Gibbs, American Journal of Science, vol. xxii. April, 1882.
' H. A. Lorentz, Wied. Ann. t. ix.; Schlomilch. ZeiUcUrift, t. xxiii.
256 EEPOET — 1885.
same as that of tlie regular or average displacement, but the relations
between ^, ??, ^ and H , r\' , C change rapidly as we pass from point to point of
the element.
The velocity of wave propagation is found by equating the maximum
potential and kinetic energies of the medium. It is shown that the
equations lead to Fresnel's constiuction in the case of a crystal if the
solenoidal condition be assumed, while the relation between f.i the refractive
index and \ the wave length is given by
1 _ H 2w,H.'
y^2Kk'^ x^ .... (^u>
H, l\ and H' being constants. The objection which Briot made to
Cauchy's theory of dispersion may be made to this. We should expect
dispersion in a vacuum as well as in ordinary transparent media.
The properties of circularly polarising media are discussed in a second
paper,' in which I', r/', ^' are treated as linear functions of s, jy, ^ and their
differential coefficients ; and in a third paper the fundamental equations are
reestablished in rather a more general form than that given by Maxwell.
The generality is gained partly by dealing with the average values of
the various quantities, and partly by supposing that the relation between
the E.M.F. and displacement is given by
[E] = [tj] + >// [U] : . . . (21)
^ and </' being two arbitrary functions, and [ ] indicating that the average
value is taken. In the simple theory ^ is a constant, and equal to 47r/K,
and ^ zero, and this will not give dispersion.
There seems, however, to be no reason — as has been pointed out by
Professor Fitzgerald — against applying to the oscillations of the electro
magnetic field the methods and reasoning developed in the third part of
this report. Almost the whole of the woi'k can be translated into the
lanouage of the electromagnetic theory at once. Periodic electric dis
placement in the ether will produce periodic electric displacement in the
matter, and the relations between the two will depend on the ratio of the
period of the ether vibrations to the possible free periods of the electric
oscillations in the matter molecules ; and it is not difiicult to see how the
action between the two might depend on the relative electrical displace
ments and their differential coefficionts.
§ 2. MaxwelP has given a theory of the magnetic rotation of the plane
of polarisation on this theory. He assumes (1) that the effect of mag
netic force is to set up molecular vortices in the medium ; (2) that the
components of the magnetic force obey the same law as the components
of the strength of a vortex in hydrodynamics; and (3) that there arises
in the value for the kinetic energy of the medium a term of the form
2C(awi + /3w2 + ywj), w,, W2, ^3 being the components of the angular
velocity, and a , /3, y of the magnetic force.
For the case of waves travelling parallel to z the kinetic energy is
shown to be
T = i^>(^2 + f,^ + i^) + cy(.) g  ig) . . (22)
' J. W. Gibbs, American Journal of Science, vol. xxiii. June, 1882.
« Maxwell, Electricity and Magnetism, vol. ii. p. 40.
ON OPTICAL THEOKIES. 257
and tlie equations of motion,
From this it follows that the rotation per unit length is
fl = „„,;l(i_x) .... (24)
where i is the index of refraction, and this formula agrees well with
experiment.
It should be noticed that in obtaining this formula Maxwell deals
with the displacements of an ordinary medium ; the forces assnnied are
those arising from the elastic reactions of this medium, the vortex motion
in which is connected with the magnetic force. The displacements are
not treated as identical with the electric displacements, nor is any indi
cation given of the connection between the two.
§ 3. Fitzgerald, in the paper already mentioned, applies the theory to
the case of reflexion from a magnetic medium. He finds that when
plane polarised light is reflected directly from such a medium, the
reflected light is slightly elliptically polarised. This is not in accordance
with Kerr's experimental result, but Fitzgerald treats the iron as a trans
parent, or nearly transparent, substance with a real refractive index.
§ 4. It was shown by E. H. Hall that when a current passes across
a conductor in a magnetic field an electromotive force is produced whose
strength is proportional to the product of the current and the strength of
the field, and whose direction is at right angles to the plane containing
the current and the field.
By introducing into the equations for the electromotive force terms
expressing this, so that they become
^=%^^{ygfth) .... (25)
at p
etc., Prof. Rowland ' has calculated the magnetic rotation of the vectors
F, G, H, and, on the assumption that a similar efiect will be produced
in a dielectric, arrives at the same formula as that given by Maxwell.
§ 5. The main difBculty of the theory, and the one which stands most in
the way of its general acceptance, is the diSiculty of forming a clear phy
sical idea of what electric displacement is, and various analogies have been
suggested with a view to rendering the difficulty less serious. One of these,
due to Helmholtz,^ is developed in a paper on the molecular vortex theory
of electromagnetic action.^ It is shown there that, if the components of
the magnetic force be identified with the molecular rotations in a con
tinuous medium in which the displacements are s, v, C, then the compo
nents of the electrokinetic momentum are equal to J^^l, etc. ; and the
equations of the electrical field in a conductor would imply that the
medium in the conductor has the properties of a viscous fluid, while in a
dielectric, so far as the motion to which the undulatory effects are due is
' Eowland, Phil. Mag. April, 1881.
 Helmholtz, Crelle Journal, t. Ixxii.
^ Glazebrook, Phil. Mag. June, 1881.
1885. a
258 KEPOET — 1885.
concerned, its properties are those of an elastic solid in which the elec
trical displacement / is given by
^'/=v^'+i(4;40 . . . w
The objection that it is impossible to maintain a continuous molecular
rotation in an elastic solid may be made to this analogy. It seems, how
ever, possible that, as suggested by Professor Stokes when considering
the problem of aberration, the ether may behave as a perfect fluid for all
motions involving more than a very small relative displacement of its
parts, while for such small displacements as are contemplated in the
theory of light it has, in a dielectric, an appreciable rigidity. In a con
ductor the effects of this rigidity, if it exist, are masked by the more
powerful effects of the viscosity. The fluid is no longer perfect.
Chapter IV. — Rowland's Theory of the Peopaqation of Plane Waves.
§ 1. The propagation of waves of electromagnetic disturbance from
a given source has been recently very fully considered by Professor
Rowland,' and we proceed to give some account of his paper.
Rowland considers very generally the solution of the equations —
^=V2v2F, (27)
etc., and allied equations given by the system
F. + , ='^'^' .... (28)
so that F, G, H satisfy the solenoidal condition. He puts
^_(,„+i) being a spherical harmonic, and C„ a function of p.
He finds
^^+2(ai6)^?a.JiOM:l)c,.=0
dfj^ dp p^
whence
f nn+1 n{n'^l'') (n+2)
C„Col^^ +^^5 ^" +  •
where c = a — ib.
He then takes, as a special solution,
etc., and treats the case of symmetry round the axis of x, for which
^ _ ( i)"Q. i
p"n!
Q„_, being a zonal harmonic with the axis of x for axis.
' Rowland, American Joxi/rnal of Mathematics ; Phil. Mag, June, 1884:.
•
(29)
•}
(30)
.
(31)
•
(32)
ON OPTICAL THEOEIES. 259
Let be tlie angle between this direction and that to the point at which
the disturbance is required, p the distance to the point, and a the angle
between the plane xOp and some fixed plane.
Let 0', 9" denote disturbances perpendicular to the radius vector in
the plane xOp,
P' P" along the radius vector, and
N' N" normal to the wave plane xOp.
Then it follows that if we have small electric displacements X'e~'*'^~^'"
parallel to x throughout the small sphere (fTrR' = dv), that
e' =  2^0+^2 gX' ^.^ Q^_ a^vn^,, \
L/Q bp
P'= ^3!^'cos0e'^O'V'>(Zi;  '
Co 4Tp2 )
N' = 0" = P" =
j^„^3&^X^sin0C,^_,,,,_v„^ 1 .... (34)
0, = 0.(1^1)
3i 3^^• • • ■ (35)
where
C,=
 ^° G  4~by)
This agrees with the results given by Stokes and Lord Rayleigh, already
quoted,' N" being proportional to the rotation. The effect of a general
arbitrary electric and magnetic displacement is then found.
In considering the optical problem it is pointed out that electric
displacement is always accompanied by magnetic, and that the effects of
the two must be considered, and according to the views of Professor
Rowland the two must be considered independently. From the relation
between the electrostatic and electromagnetic energy, it follows that if
there be an electric displacement X'e*^' there will be a magnetic Y"e'"''
where
Y" = ^X'.
The electric displacement at any other point of space is found and
expressed as below. Let the origin be the point at which X', Y" act ; the
axis of z the normal to the plane of X'aY" ; p the direction in which the
effect — at a point A — is required ; the angle 2OA = d, and the angle between
zOA and zOx = ^ ; and let P', 0', 4>' be the displacements along OA, and
normal to 6 and f.
Then
e' ='!pT cos <p [a + COS d)(l i]  e^l e':^o.vo ^
8'^P ^[_^ T ^\^ j^; ^2^2]^^ [(36)
P'= ^4^8in0cos9.ri_lV'^^v«
47rp2 r ^ ^^j
' See p. 201.
82
260 EEPOET — 1885.
And we can show that in the value of 6' it is the 1 in (1 + cos 0) which
comes from the assumed magnetic disturbance, while in <S>' it is the cos d
in the same term.
The magnetic disturbance produces no effect in the value of P' . Neglect
ing the magnetic disturbance we arrive at Stokes's result for the effect of
a disturbance X'e''^'* on the medium, which is used by Rayleigh in the
paper on the blue of the sky.
Now we may note that the result of the experiments on scattered
light seems to disprove this hypothesis of Rowland's as to the necessity of
considering the two disturbances, for according to him the intensity is the
same at all points in the plane xy at the same distance from O. This is
not true ; the intensity varies as sin^a if a is the angular distance of the
point from the axis of x. Again, it is true, of course, that the magnetic
disturbance accompanies the electric, but it accompanies itas a consequence.
If we produce, by some impressed force, a varialale electric displacement
at a point in the medium, and calculate the effect due to this, we have
done all that is necessary. There will, it is true, be magnetic displace
ment, but it can be calculated from the electric.
Rowland's results do not apply to the case of a wave being propa
gated through an aperture, for in this case we have no right to assume
that the disturbance produced by an element is symmetrical round
the direction of vibration . We have not a single particle or an indefi
nitely small sphere vibrating and sending out its effects in spherical
waves ; we have a state of motion coming in from behind the aperture,
and being continually propagated across it at a given point P and at
time to, we must consider the circumstances at any point O of the
aperture at a time t^ such that OP = &(i — fo) For these will be the
initial circumstances so far as we are concerned ; and at this time t^,
has an initial velocity and an initial displacement, Both these require to
be considered in dealing with the question, and we have to adopt Stokes's'
method of solution, and we again arrive at his theorems with regard to
the relation between the direction of vibration and the direction of
diffraction.
§ 2. The electromagnetic theory, if we accept its fundamental hypo
theses, is thus seen to be capable of explaining in a fairly satisfactory manner
most of the known phenomena of optics. The great difficulty is, as we
have said, to account for the properties which the medium must have in
order to sustain electrical stresses. These consist in an electrostatic field
of a hydrostatic pressure KR^/Stt, combined with a tension KR^/47r
along the lines of force ; R being the resultant electrical force, and K
the inductive capacity. There will therefore be a difference of pressure
in different directions in the ether.
Combined with this difficulty there is another of a similar kind, that
of realising mechanically what electric displacement is, of forming for
oneself a physical idea of a change of structure in some medium of
unknown properties which shall obey the laws implied by the various
equations satisfied by the components of electrical displacement.
Optical effects are certainly due to changes, periodic in space and I
time, of some properties of a medium which we call the ether. Electro
magnetic effects are also due to variations in properties — it may be the
same as those which give rise to light — of the same ether. When the
' On this point reference has already been made, see p. 206.
ON OPTICAL THEOEIES. 261
electromagnetic effects become rapidly periodic they travel with the
velocity of light, and the direction to which the change of property is
related is in the wave front, at least for isotropic media.
The rigidity or quasirigidity through which the medium has the
power of propagating these transverse waves of small displacement may
be given to it through other motions which are going on independently
of the light. The free passage of the planets through space proves that
it can have little if any viscosity or rigidity, though, according to the
views of Professor Stokes, while behaving as a perfect fluid for all
appreciable motions, it might conceivably be rigid for the very small
displacements in a lightwave. Taking Sir W. Thomson's estimate of
the density of the ether as about 10"^ grammes per cubic centimetre, the
rigidity required for the propagation of light would be about 10""^ The
rigidity of glass is about 25 X 10". While it might, then, be conceivable
that the ether should have this very small rigidity and yet ofier no
appreciable resistance to the earth's motion, it is difficult to reconcile
this with its power of standing electric stress, and we are forced to con
clude that the change implied in electric displacement is much more
than a mechanical displacement of the molecules of a perfect fluid. A
qnasirigidity might be conferred on the fluid by filling it with vortices,
and it might thus become capable of conveying transverse waves and of
standing electric stress. Electric and magnetic polarisation would then
consist in definite arrangements of the vortex rings or filaments. Changes
in these arrangements, or in some of the properties connected with them,
would constitute electric and magnetic displacements, and possibly also
h'ght.
We should then have a complete electromagnetic theory of optics, or
rather a complete theory of the ether embracing electromagnetism and
optics, but towards this theory our present knowledge has made only a
small advance.
Report of the Committee, consisting of Professors Ramsay, Tilden,
Marshall, and W. L. GtGODwin (Secretary), appointed for the
purpose of investigating certain Physical Constants of Solution,
especially the Expansion of Saline Sohdions.
TocR Committee have to report as follows :
They have obtained apparatus for determining the rates of expansion
of saline solutions fiom 20° C. to f60° C.
They have devised experiments for determining the distribution of a
weighed quantity of water between molecular weights of two salts, the
three substances being placed in separate vessels in the same enclosed
space kept at a constant temperature.
But further progress in either of these directions was interrupted by
the continued illness of one of the Committee.
Your Committee respectfully ask for reappointment.
262 EEPORT— 1885.
Third Report of the Committee, consisting 0/ Professors Williamson,
Dewae, Frankland, Crum Brown, Odling, and Armstrong,
Drs. Hugo Muller, F. E. Japp, and H. Forster Morley, and
Messrs. A. Gr. Vernon Harcourt, C. E. Groves, J. Millar
Thomson, H. B. Dixon (Secretary), and V. H. Veley, reap
pointed for the purpose of dratuing up a statement of the
varieties of Chemical Names ^vhich have come into use, for
indicating the causes tvhich have led to their adoption, and
for considering what can he done to bring about some conver
gence of the views on Cheriiical Nomenclature obtaining among
English and foreign chem,ists.
An account of tlie authorship of some of the various systems of nomen
clature which have been devised for the purpose of distinguishing between
compounds formed by the union of the same elements in different propor
tions, has been given in the ' Historical Notes ' prefixed to the Second
Report of this Committee. Among these systems the use of the termina
tions oMs and ic, to denote respectively lower or higher degrees of saturation
of one element or group with another element or group, is perhaps that
which has met with the widest acceptance. This system further directs
that when electronegative groups, the names of which end in ous and ic,
unite with electropositive groups to form salts, these terminations are to
be changed into ite and ate respectively.
Before proceeding to discuss the practical application of this system,
it may bo well to point out, as a minor etymological detail, that the literal
meaning of the terminations ous and ic has altered since they were first
employed. Thus ous (Latin osus) ought to denote, on the part of the
compound, richness in that element to the name of which the termination
is attached. For example, cujirous (cuprosus) means ' rich in copper ' :
cuprous oxide is primarily an oxide which is richer in copper than cupric
oxide, and only by implication an oxide which is poorer in oxygen. This
implied signification is, however, that in which the name cuprous oxide
is nowadays employed. A curious result of this change of literal meaning
is to be found in the use of the prefix hypo to denote a still lower degree of
saturation than that expressed by ous. Thus the name hyponitrous acid
is taken to denote an acid containing still less oxygen than nitrous acid ;
whereas hyponitrous really means ' less rich in nitrogen,' which is the vdty
opposite. Had the etymology been logically carried out, the prefix ought
to have been hyper. A similar confusion of ideas is displayed in the use
of the prefixes hyper and per at the other end of the scale ; in place of
these, hypo ought to have been employed. Ferchromic acid does not, as
its name literally taken signifies, contain more chromium than chromic
acid : it contains less, and ought consequently to have been termed
/typochromic acid.
It need hardly be said that it would be illadvised to attempt to
change a system so firmly established as that involved in the present
use of these prefixes hypo and hypier ; and in the above remarks on
the etymology of the subject, nothing of the kind is intended. No
ambiguity can arise from the use of terms about the meaning of which
everyone is agreed, and their mere etymological accuracy is, in view of
this allimportant consideration, of secondary importance.
ON CHEMICAL NOMENCLATUBE.
263
The following list will show the application of the ic and ous nomen
ilature to salts and salifiable oxides : —
I. List of Salts where Two or more Series of Compounds are formed.^
Name denoting metallic
Formula of corre
Name denoting metallic
Formula of corre
radical of salt
sponding oxide
radical of salt
sponding oxide
Cuprous
Cu.O
Chromous
CrO
Cupric
Cub
Chromic
Cr„03
Mercurous
Hg,0
Uranous
u6„
Mercuric
HgO
Uranic ( tJranylic)
UO3"
Aureus
Au„0
Manganous
MnO
Auric
Au„03
Manganic
Mn,03
Thallous
Tlo'O
Ferrous
Feb
Thallic
TLO3
Ferric
Fe,03
Stannous
Snb
Cobaltous
CoO
Stannic
SnO„
Cobaltic
Co„03
Cerous
CeoO'a
Platinous
PtO
Ceric
Ceb„
Platinic
PtO^
Names corresponding with ijlatinous and platinic would be applied to
the corresponding oxides and salts of the other metals of the platinum
gi'oup — distinguishing, however, the other oxides and salts of this group
by numeral or other designations.
The designations given in this Table to the various higher and
lower series of salts and salifiable oxides have been employed with almost
complete uniformity by all chemists who have adopted this system of
nomenclature.
As a metal rarely — if ever — forms more than two salifiable oxides, the
ous and ic terminations generally suffice for purposes of distinction so far
as the salts of metals are concerned.
The practice of further employing these terminations in the case of
acidforming oxides does not lead to confusion, since these oxides are
distinguished by the name anhydride (or acid).
CrO Cr^Og
Chromous oxide.
Thus we have
Cr03
Chromic oxide. Chromic anhydride
(Chromic acid.)
Indifferent oxides have frequently been classified and named by
regarding them as compounds of salifiable, with acidforming oxides,
CrjO^ being termed chromic chromate. For stages lower than ous, the
prefixes hi/po and sub are employed. Custom appears to have restricted
hypo chiefly to acids and to acidforming oxides, suh to salifiable and to
indifferent oxides.
With regard to the termination o^is, the minor question arises, how
far this termination ought to be written in the forms ious and ecus.
The answer is : as seldom as possible. ' Cupreous ' has generally given
way to ' cuprous ' ; no one writes ' chromious ' (although the name of
the metal is ' chromium ') ; and there is no reason why such names as
' ruthenious ' and ' iridious ' should not equally be shorn of their super
fluous penultimate syllable.
A further question, concerning which considerable difference of opinion
has prevailed, is whether any ous or ic terminations ought to be
employed in the names of salts of which only one class is known — thus
magnesic sulphate instead of magnesium sulphate. There is something to
' In this list the term ' salt ' is taken to include ' haloid salts,' but to exclude the
halogen compounds of those elements whose oxides do not yield oxysalts with acids,
264 . EEPORT — 1885.
be said here for both systems ; and, as the diversity of practice does not lead
to confusion, and conseqnently does but little harm (beyond in each case
offending the ears of those accustomed to the opposite system), the ques
tion need not be regarded as a vital one. Objections which have been
urged against the use of any termination in such cases are that chemists
have not always been able to agree as to which termination is to be used
in a given case, and that, apart fi"om this, the practice causes beginners
erroneously to surmise the existence of a second series of salts. The
objection on the other side is that the omission of the terminal ' ic ' breaks
the uniformity of the system and leads beginners to suppose that barium
sulphate, for instance, has a different constitution from cupric sulphate.
In the case of carbon compounds, on the other hand, there is a distinct
advantage in aflSxing ic to the names of the positive radicals in ethereal
salts. A neglect of this precaution leads to ambiguity — at all events in
the spolcen name. Thus, though tliere is no ambiguity in the name etlujl
loTienijlacetate when written, yet the ear cannot distinguish between it and
etlujlpTienyl acetate. This ambiguity is obviated by the use of the termi
nation ic : thus, eilnjlic plienylacetate and efJiylphenylic acetate.
In the use of the terminations ous and ic to distinguish different series
of acids and acidforming oxides, the practice of chemists has also been
very uniform. Indeed, with the exception of one or two isolated cases
almost perfect unanimity has prevailed.
To sum up, the ous and ic terminations when employed for purposes
of distinction in cases where two series of oxides, acids, salts, &c., are
known, have been almost free from ambiguity, and for this reason
deserve to be retained. On the other hand, in cases where only one series
is known, those chemists who have employed one or other of these
terminations have occasionally differed as to which ought to be used :
the difficulty may be solved, as it has been done by some chemists, by
avoiding the use of any termination in such cases.
In complex cases where the above modes of naming prove inadequate,
recourse may be had to numeral designations. These appear especially
admissible in cases where an oxide occurs which is intermediate between
the ous and ic stage, and at the same time cannot be classed as a com
pound of oxides already classified and named.
In applying numeral designations, it is most important to select only
such as are free from hypothesis and which afford correct information.
In this respect, chemists appear of late years not to have been sufficiently
careful. As an example, arsenious oxide may be quoted ; this compound
is frequently termed 'arsenic trioxide,' the formula being written AsgOj,
and it is tacitly assumed that the molecule contains three oxygen atoms.
There are three objections to this name: — (1) That, assuming the formula
on which it is based to be correct, it affords no information as to the
number of arsenic atoms associated with the three oxygen atoms ; (2)
that it involves the assumption that arsenious oxide does not vary in
molecular weight, whatever its physical state ; and (3) that the formula
of gaseous arsenious oxide is AS4O6.
In employing numeral designations to indicate molecular composi
tion in cases where this is established, it is therefore important to express
the number of atoms of each constituent element, as dicarhon hexachloride,
C2 Clg. But in the case of solid and liquid bodies of which the molecular
weight is either unknown or may vary with temperature, the name
should indicate merely the relative proportions in which the constituents
are associated ; or, more explicitly, the name should indicate the proper
ON CHEMICAL NOMENCLATURE. 265
tion of the radical associated with what may be termed the characteristic
element of the compound. No difficulty occurs in the case of the chlorides,
or analogous compounds with the monad elements generally, these being
termed mono, di, tri, tetra, penta, or hexachloride, &c., according as
combination is in the proportion of 1, 2, 3, 4, 5, or 6 atoms of chlorine to
1 atom of the characteristic element. The application of this system
would involve the use of the names tin dichloride and iron trichloride
(not sesquichloride) for stannous and ferric chlorides respectively, names
which accurately express the relative proportions of chlorine to metal in
these compounds without any hypothesis as to their molecular composition
— a composition, which in the case of the former compound, at all events,
certainly depends on temperature. It will, however, involve a slight depar
ture from the existing practice when applied to oxides, sulphides, and other
compounds of polyad elements ; thus oxides of the type (R2)"0 would
be termed hemioK.ides, since they consist of the characteristic element
and oxygen in the proportion of one atom of the former to half an atom.
of the latter. Oxides of the type (R2)"03 would be termed sesqui
oxides, since the characteristic element and oxygen are present in the
proportion of one of the former to one and a half of the latter. Oxides of
the type R2 O5 would be termed sestertioxides, as they contain oxygen
and the characteristic element in the proportion of two and a half
atoms of the former to one of the latter. Oxides of the types RO,
RO2, RO3, and RO4, would be termed respectively mono, di, tri, and
<e<roxides.
Acid Salts.
There are two distinct classes of salts to which this name has been
given : —
1. Salts with two or more metals, one of the metals being hydrogen.
2. Salts formed from these by the removal of water.
Until comparatively lately, no attempt was made to give distinctive
names to these two classes, except that sometimes the words hydratic and
anhydrous were used to distinguish them. The distinctive names —
pyrophosphate, metaphosphate — which Graham gave to the two sets of
anhydrous acid phosphates were founded on the supposition that the
phosphoric acid (PO5) existed in them in two modifications, different
from the acid of the ordinary phosphates.
The nomenclature used by nearly all chemists from the beginning of
this century until about 1860 is illustrated on tables 36. Acid salts in
which for the same quantity of base there is 2, 3, . . . &c. times as much
acid as there is in the normal salt are called hi ate, ter ate, &c. (in
German, doppelt (or zweifach) saures Salz, dreiiach saures Salz,
&c.) In English and French the Latin adverbial numerals his or hi, ter,
&c. seem always to have been used until about twenty years ago, when
Greek adverbial numerals were introduced for the anhydrous acid salts.
Watts's Dictionary and Naquet are the first English and French
authorities in which we have observed this change.
Basic Salts.
There are two distinct classes of salts to which this name has been
given : —
1. Salts with two or more salt radicals, one of the salt radicals being
hydroxyl.
2. Salts formed from these by the removal of water.
266 KEPOET— 1885.
These were not distinguished by name until quite recently, and are
still very often confused.
The nomenclature in general use is illustrated on tables 812.
Basic salts of oxygen acids in which for the same quantity of base there
is ^, ^, &c. as much acid as there is in the normal salt are called
di ate, tri (or tris) ate, &c. (in German, halb saures Salz,
drittel saures Salz, &c.)
Basic salts of oxygen acid were also named by the proportion of base
to acid, the proportion in the normal salt being taken as unity — bibasic,
terbasic, &c. salts (in German, zweifach, dreifach, etc. basische Salze).
Thus ^rt'snitrate (drittel saures salpetersaures Salz) is the same as terhasic
nitrate (dreifach basisches salpetersaures Salz), Latin adverbial numerals
being used for multiples, and Greek adverbial numerals for submultiples.
The compounds of basic oxides with haloid salts (corresponding to
the basic salts of the oxygen acids) are variously named ; thus, oxy
chloride, bisoxychloride, basic chloride, bibasic chloride. The numerals
here refer not to the number of atoms of oxygen and halogen, but to the
proportion of metal combined with oxygen and halogen respectively
(or perhaps more correctly to the proportion of equivalents of oxygen and
halogen) ; thus 2PbO.PbC]2 is bisoxychloride, or bibasic chloride. It is
to be noted that corresponding basic haloid and oxygen salts have not the
same numeral ; as —
PbO.PbClo is basic chloride (einfach basisches Chlorid).
PbO.Pb(N03)9 is bibasic nitrate (zweifach basisches Salz), because
it is 2PbO.]Sr20g.
2PbO.PbCl2 is bibasic chloride (zweifach basisches Chlorid).
2PbO.Pb(N03)o is terbasic nitrate (dreifach basisches Salz), because
it is SPbO.NgOs
Sulphur Salts. — Table 14.
These have sometimes, especially in German, been named as double
sulphides, but usually, in Latin, English, French, and recently also in
German, follow the names of the corresponding oxygen salts.
Sulphur Basic Salts. — Table 1 3.
Compounds of normal salts with sulphides of the metal. These were
discovered by H. Rose, and called by Berzelius sulphur basic (schwefel
basisch), as corresponding to the compounds of normal salts with the basic
oxide. This nomenclature has not been generally adopted, and, as will be
seen from the table, there is little uniformity in naming these substances.
Double Salts.
With very few exceptions, these may be classified in two sets.
1. With a common salt radical. 2. With a common metal. 1. With a
common salt radical. Here again there are two kinds, (a) Salts of
polybasic acids. (6) Compounds of two haloid salts, or of a haloid salt,
with a compound of a halogen and a non metallic element.
(a) These are named consistently with the names of the simple salts j
as phosphate of magnesia and ammonia, phosphorsaure ammoniak
magnesia, magnesium ammonium orthophosphate, ammonic magnesio
phosphate, or, with what may perhaps be called an adverbial modification
of the first adjective, ammoniomagnesic phosphate.
(h) Of these we may take as examples 2KF, Sir4 ; 2KC1, PtCl4 ;
2KCN, Pt(CN)2; KF, BF3 ; KCl, AuClg ; 4KCN, Fe(CN)2 ; 3(KCN),
Fe(CN)3. See Tables 15, 16, 17.
ON CHEMICAL NOMENCLATURE.
267
These have been named on three different principles : —
(a) As double fluorides, chlorides, etc. ; for instance, fluoride of silicon
and potassium, fluorkieselkalium. T!^T
(fi) As compounds of the positive metal with a compound salt radi
cal ; for instance, ferrocyanide of potassium, silicofluoride of potassium,
kieselflu orkalium .
(7) As analogues of oxygen salts ; for instance, fluosilicate of
potassium, potassium fluosilicate, potassium chlorplatinate, chloraurate,
cyanaurate.
The third system seems only to be used when there is really a corre
sponding: oxygen compound.
2. With a common metal. As a wellknown substance mentioned by
most systematic writers, emerald green has been selected — table 18.
It will be seen that where a name is given, it is either acetate and
arsenite, or a combined name, acetoarsenite, or arsenigessigsaures Salz.
List of Authorities referred to hy their nurribers in, thefolloioing tables.
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Author
Thomson . .
Thomson . .
Thomson . .
Brande . . .
Thomson . .
Brande . . .
Ongren (Table to
Berzelius)
Brande ....
Graham . . .
Gmelin ....
Liebig (Geiger) .
Mitscherlich .
Handworterbuch
Kopp's Geschichte
(vol. iv.)
Kane
Graham . . . .
Eegnault . . . .
Fownes
Otto
Edition
Date
No.
20
II.
1804
IV.
1810
21
V.
1817
22
I.
1819
23
vir.
1831
IV.
1837
24
IV.
1838
25
26
V.
1841
27
I.
1842
28
IV.
18434
29
V.
1843
30
IV.
1844
I. & II.
184864
31
—
1847
32
II.
1849
33
II.
18.50 &
1858
34
III.
1851
35
V.
1854
36
III.
185560
Author
Miller
Eegnault . . . .
Rose (French) . .
Watts's Dictionary
and Supplements
Naquet ....
Eose (Finkener)
Fownes . . .
Williamson . .
Wurtz's Dictionary
Bloxam ....
Eegnault Strecker
Wislicenus
Kolbe, Kurzes Lebr
buch
Fownes
Miller
Eoscoe and Schor
lemmer
Frankland and Japp
Kolbe (Humpidge).
Edition
Date
I.
1856
V.
1859
—
1862
—
186381
II.
1867
VI.
186771
X.
1868
II.
1868
—
186976
II.
1872
IX.
1877
—
18778
XII.
1877
VI.
1878
—
187881
_
1884
"
1884
1. Muriat of lime.
2. Muriate of lime.
3. Chloride of calcium (also muriate of
lime).
4. Chloride of calcium.
5. Chloride of calcium.
6. Chloride of calcium (cal + C).
7. Chloretiim calcicum (CaCl).
8. Chloride of calcium or muriate of
lime (Cal+C).
9. Chloride of calcium (CaCl).
10. Chlorcalcium (CaCl).
11. Chlorcalcium (calcium chloratum)
(CaCl,).
12. Chlorcalcium (CaCl).
13. Calciumchlorid, chlorcalcium (Salz
saurer Kalk) (CaCi), 1859.
14. Chlorcalcium.
15. Chloride of calcium (CaCl+6Aq).
16. Chloride of calcium (CaCl).
17. Cblorure de calcium (CaCl).
18. Chloride of calcium (CaCl).
19. Chlorcalcium (CaCl).
Chloride of calcium.
Chlorure de calcium (CaCl).
20.
21.
22.
23.
24.
25.
Chloride of calcium (CaCL).
S upp . C alciu m cliloride .
Chlorure de calcium.
Chlorcalcium.
2nd
268
REPORT — 1885.
26. Calcium chloride (CaClj).
27. Calcic chloride (CljCa).
28. Chlorure de calcium.
29. Chloride of calcium (CaClj).
30. Chlorcalcium (CaCL).
31. Chlorcalcium (Ca"Cl2).
32. Calcium chloride (CaCl,).
1. Sulphat of soda.
2. Sulphate of soda.
3. Sulphate of soda.
4. Sulphate of soda.
5. Sulphate of soda.
6. Sulphate of soda (S + .s')
7. Sulphas natricus (Na S)
8. —
9. Sulphate of soda (NaO,S03+ lOHO).
10. Einfach schwefelsaures Natron.
11. Schwefelsaures Natron (natrum
sulphuricum) (NaO,S03,10Aq).
12. Schwefelsaures Natron (NaS + lOAq).
13. Schwefelsaures Natron, neutrales,
1859.
14. Schwef(;lsaures Natron.
15. Sulphate of soda (NaO.SOa + lOAq).
16. Sulphate of soda (NaO.SOa).
17. Sulfate de soude (NaO,S03).
18. Sulphate of soda (NaO.SOa).
19. Schwefelsaures Natron (NaOjSOj).
20. Sulphate of soda (NaO.SO,).
21. Sulfate de soude (NaO.SOj).
33. Calcic chloride (or chloride of cal
cium) (CaCU).
34. Calcium chloride (chloride of cal
cium) (CaCl.,).
35. Calcic chloride (CaCU).
36. Calcium chloride (CaClj).
n.
22. —
23. Normal or neutral sulphate of
sodium. 2nd Supp. sodium sul
phate (Na.SOJ.
24. Sulfate neutre de soude.
25. Schwefelsaures Natron.
26. Sodium sidphate (SO^Naj)
27. Sodic sulphate (Na.SOJ.
28. Sulfate neutre de sodium.
29. Sulphate of soda (NajO.SOj).
30. Neutrales schwefelsaures Natrium,
Oder Dinatriumsulfat (Na^SO^,
lOH^O).
31. Schwefelsaures Natron, neutrales
32. Sodium sulphate.
33. Sodic sulphate, or sulphate of
sodium (Na^SOj).
34. Normal sodium sulphate (also sul 1
phate of soda).
35. Sodic sulphate (SOjNaOj).
36. Sodium sulphate.
III.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
Supersulphate of soda.
Bisulphate of soda.
Bisulphate of soda.
Bisulphate of soda.
Bisulphate of soda.
Bisulphate of soda.
Bisulphate of soda
0,S0,).
(H0,S03 + Na
Saures (od. doppelt) schwefelsaures
Natron (NaO,2S03 + Aq).
Schwefelsaures Natron und schwefel
saures Wasser, zweifach schwefel
saures Natron (NaS + 3H = NaS +
HS + 2H).
Schwefelsaures Natron, zweifach
saures, wasserhaltendes Salz
(NaO,S03 + HO,S03).
Saures schwefelsaures Natron.
Bisulphate of soda (NaO,S03 + HO,
SO3).
Bisulphate of soda (HO.SOs + NaO,
SO3).
Bisulfatede soude (NaO.SO^t HO.SO'
+ 2H0).
18. Bisulphate of soda (NaO.SOa + HO,
SO3 + 3H0).
19. Zweifach schwefelsaures Natron,
Wasserhaltiges (NaO,S03 + HO,
SO3).
20. Bisulphate of soda (NaO,HO,2SO,').
21. Bisulfate de soude (NaO.SO» + H0.
S0» + 2H0).
22. Bisulphate de soude.
23. Hydromonosodic sulphate (hy
drated bisulphate of soda) (NaH
SO,).
24. Bisulfate de soude.
25. Saures schwefelsaures Natron.
26. Sodium and hydrogen sulphate, or
acid sodium sulphate (2S04NaH.
3OH2, or SO,Na2.SO,H,.30H2).
27. Hj'drosodic sulphate (NaHSOj).
28. Sulfate acide de sodium (SO^NaH).
29. Bisulphate of soda (Na20,H20,2S03).
30. Mononatrium Sulfat, oder halbge
siittigtes saures schwefelsaures
Natrium.
31. Saures schwefelsaures Natron fONa
S0„10H
32. Sodium and hydrogen sulphate, 01*
acid sodium sulphate (see 26). ,
S3. Hydric sodic sulphate (acid sulj
ON CHEMICAL NOMENCLATURE.
269
pliate of sodium or bisulphate of
soda) (NaHSO^).
34. Hydiogen sodium sulphate (NaH
SOJ.
35. Hydric sodic sulphate (SO^HoNao).
36. Acidsodium sulphate S0„ f {qm ")
IV.
1.
2.
3.
4.
5.
6.
7.
8.
9.
iio.
11.
I 12.
I 13.
' 14.
15.
16.
17.
18.
19.
See Table III.
Anhydrous bisulphate of soda (S +
2s')
Bisulphas iiatricus Na iS.^.
Anhydrous bisulphate of soda (S
+ 2s').
Zweifach schwefelsaures Natron
(NaO, 2SO3).
Saures (doppelt) schwefelsaures Na
tron, das wasserleere Salz.
Schwefelsaures Natron, zweifach
saures wasserfreies Salz.
(Not specially named.)
Anhydjous bisulphate (a true bisul
phate).
Un veritable bisulphate (Na0.2S03).
Anhydrous bisulphate of soda (NaO,
2.SO3).
Zweifach schwefelsaures Natron,
wasserfreies Salz (NaO,2S03),
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
Bisulphate of soda, the anhydrous
salt.
Un veritable bisulphate (Na0.2S0').
Anhydrosulphate of sodium or an
hydrous bisulphate of sodium
(Na„S.,0. = Na„S0„S03 = Na„0,
2SO3) 1875.
Disulfate de sonde.
Anhydro bisulphate (S0,Na„,S03).
Sodic disulphate (NaoS^O,).'
Anhydrosulfate.
Neutrales Kalium Pyrosulfat.
Dischwefelsaures Natron
/^/SO,ONa\
\^ \,SO.,ONaj
Pyrosulphate (NajSoO, or Na„SO,,
SO3).
Sodic pyrosulphate (Na^S^O,).
Sodium disulphate (Na.SJO,).
Sodic pyrosulphate (S^O^NaOo).
Sodium disulphate (0{«ggNa^J
V.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
(Alkaline chromats.)
Chromate of potash [red colour].
Bichromate of ijotash.
(Not distinguished from chromates.)
Bichromate of potash.
Bichiomate of potassa (2Chr' + P).
Bichromas kalicus (KCro).
Bichromate of potassa (2Chr' + P).
Bichromate of potash (KO,2Cr03).
Not mentioned.
>> >>
Zweifach chromsaures Kali.
Doppeltsaures od. rothes chrom
saures Kali (KO,2Cr03), 1859.
Bichiomate of potash (KO + 2Cr03).
Bichromate of potash (KO,2Cr03),
_ 1858.
Bichromate de potasse.
Bichromate of potassa (KO,2CrOg).
Zweifach od. rothes chromsaures
Kali (KaO,2Cr03).
Bichromate of potash (KO,2Cr03).
Bichromate de potasse.
Acid chromate of potassium, di
chromate of potassium, or bi
chromate of potash (K„0.2Cr03
 K2CrOj,Cr03), 1863. Potassium
dichromate (K20.2Cr03), 1872.
24. Dichromate de potasse.
25. Saures chromsaures Kali.
26. Potassium bichromate or anhydro
chromate (2Cr03,K.O, or CrO.K,,
CrOg).
27. Potassic dichromate (K„Cr,0,).
28. Bichromate de potasse (K„0,2Cr03).
29. Bichromate of potash (K„0,2Cr03).
30. Kalium dichromat.
31. (Neutrales) Dichromsaures Kali.
/f. (CrO,OK\
\^ lCrO„OKj
32. Potassium bichromate or anhydro
chromate (2Cr03,KoO, or CrO.K,,
Cr03).
33. Potassic dichromate, pyrochromate,
or anhydrochromate (K„0,2Cr03,
or KXr^O,).
34. Potassium dichromate, or bichromate
of potash (KoCr^O,).
' ' / (CrO^Ko N
35. Dipotassic dichromate (JO )
\ (CrO„Ko /
36. Potassium dichromate.
270
REPORT 1885.
VI.
1. —
2. —
3. —
i. —
5. —
6. —
7. —
8. —
9. Terchromate of potash (KO.SCrOj).
10. —
11. —
12
13
14.
15.
16.
17.
18.
19.
20.
21.
22.
Dreifach chromsaures Kali.
Dreifach chromsaures Kali (KO,
SCrO^).
Terchromate of potash (KO.SCrOs)
[1858].
Dreifach chromsaures Kali (KaO,
SCrOj).
Terchromate of potash (KO.SCrOj).
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
Hyperacid chromate or trichro l
mate of potassium (K„0,3CrOs
or K2Cr04.2Cr03 [1803], po
tassium trichromate (K20,3Cr03)
[1872].
Potassium trichromate (3Cr03,K,0,
or CrO^K„,2Cr03)
Terchromate of potash (KjO.SCrOj),
Kalium trichromat.
Potassium trichromate (3Cr03,K,0,
or CrO.,K„,2Cr03).
Potassic trichromate (K„0,3Cr03).
Potassium trichromate (K^CrjO,,,).
'CrOaKo
35. Dipotassic trichromate
36.
VII.
1.
2.
3.
4.
5.
6.
7.
8.
10.
11.
12.
13.
14.
15.
16.
17.
18.
Bichromate of chloride of potas
sium.
Bichromate of chloride of potas
sium.
Bichromate of chloride of potassium
(KCl(2Cr03).
Chromsaure und Chlorkalium (KGl i 2
Cr).
Zweifach chromsaure Chlorkalium,
chlorchromsaure Kali (KGl,2Cr03
Oder KO,Cr03.CrO„ei oder 3(K0.
Cr03) + (CrGl3.2Cr03).
(KCl, + 2Cr03).
Bichromate of chloride of potassium
(KCl + 2Cr03).
Bichromate de chlorure de potassium,
or chlorochromate de potasse
(KC1.2CrO=').
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
Zweifach chromsaures Chlorkalium
(KaCl,2Cr03).
Bichromate of chloride of potassium
(KCl,2Cr03).
Bichromate de chlorure de potas
sium, or chlorochromate de potasse.
Chromochloride of potassium, 1863.
Potassium chromatochloride,
1872.
Potassium chlorochromate, 1875
L and 1879 (KCl,Cr03).
Bichromate de chlorure de potassium.
31. Chlorchromsaures Kali
32.
33.
34.
35.
36.
(crO^Sl).
Bichromate of chloride of potassium,
or potassic chlorochromate (KCl,
Cr03?).
Potassium chlorochromate (KCrOjCl).
Potassium chlorchromate.
vni.
1. Nitrat of lead.
2. Nitrate of lead.
3. Subnitrate of lead.
4. Subnitrate of lead.
5. Dinitrate of lead.
6. Dinitrate of lead (2PL i n').
7. Nitras biplumbicus (Pb^isfj.
ON CHEMICAL NOMENCLATUEE.
271
8.
9.
10.
11.
12.
13.
14.
.16.
16.
17.
18.
19.
20.
21.
22.
Dinitrate of lead ((2PL + n').
Bibasic nitrate of lead (PbO,N05 +
PbO).
Basisch salpetersaures Bleioxyd
(Pb^).
Zweifach basisch salpetersaures
Bleioxyd (2PbO,5f05, or 2PbO,
NO3.HO).
Basic salt, containing two atoms of
oxide of lead united to one of
nitric acid.
Bibasic nitrate of lead (PbO,N05 +
PbO).
Sousazotate de plomb ; azotate bi
basique (2PbO.N05+ HO).
Basic nitrate.
Halbsaures Salz (PbO.HO.PbO.NOj).
Dinitrate of lead (2PbO,N05).
(See 17).
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
Basic nitrates of lead ; diplumbic
nitrate.
Azotate basique de plomb
Basic nitrate.
Plumbic hydronitrate (PbNOaHO).
Azotate diplombique (Az03)„Pb,PbO
or parazotate, (Az20,)Pb2, or
orthoazotate (AzOi)"'Pb"H'.
Halbgesattigt hydratisch basisch
Salpetersauresblei.
Basisches Salz r^y^jOjPbY
Basic nitrate.
Dibasic plumbic nitrate (Pb2N0,,
PbHoO„).
Basic nitrate, Pb(N03)0H.
Plumbic nitrate hydrate, NO,
(OPb"Ho).
Basic salt.
rx.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
Submuriat of lead.
Submuriate of lead.
Submuriate of lead.
Oxychloride of lead.
Bibasic chloride of lead (PbCl +
2PbO), Tribasic (PbCl + 3PbO).
Einfach, zweifach, &c. basisches
Chlorblei (PbCl + PbO), &c.
Oxychloride of lead.
Oxychlorure.
Basische Bleichloride, Oxychlorid,
Bisoxychlorid, &c. (PbO.PbCl,
2PbO,PbCl, &c.)
20,
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
Oxychlorides of lead (PbO,PbCl, &c.)
Oxychlorure.
Oxychlorides (Pb^Cl^O or PbCLPbO,
&c.), 1881, III. Supp.
Oxychlorures de plomb.
Oxychlorides PbCL.PbO, &c.)
Basic plumbic chlorides (Pb.,OCL,
Fhfifi].,., &c.)
Oxychlorides of lead (PbCL.PbO,
&c.)
Diplumboxydchloriir ; Triplumb
dioxydchloriir, &c.
Basische Salze.
Oxychlorides (PbCl2,PbO, &c.)
Oxychlorides of lead (PbO.PbCl,,
&c.)
Basic chlorides (PbClj + PbO, kc.)
Oxychlorides.
Oxy or basic chloride.
X.
Subnitrate of bismuth.
Subnitrate of bismuth.
Tetartonitrate of bismuth.
Hydrated subnitrate of bismuth.
Hydrated subnitrate of bismuth.
Subnitrate of bismuth (HO.NO.
+ 3BiO).
10. Salpetersaures Wismuthoxyd, ein
fach. Basisch salpetersaures Wis
muthoxyd (Bi03,N05(Aq).
11. Basisch salpetersaures Wismuth
oxyd ; Bismuthum Subnitricum
(NA.BiO + 3Bi0,Aq.N,0.,Bi0
+ 2Bi0).
12. Verbindung von salpetersaurem Wis
muthoxyd mit Wismuthoxydhy
drat (BiN + SBiS).
272
REPOET 1885.
13. Basisch salpetersaures Wismuthoxyd,
drittelsaures salpetersames Wis
muthoxyd.
14. Basisch salpetersaures Wismuth.
15. A basic salt (BiOa + NOj).
16. Subnitrate of bismuth (BiOa.NO^
+ H0).
17. Sousazotate de bismuth.
18. Basic nitrate of teroxide of bismuth
(Bi03,N05 + 2HO).
19. Drittelsaures Salz (BiOa.NO^ + 2H0),
Bisoxynitrat
(2(Bi03,3HO)Bi03,3N05).
Subnitrate of bismuth (9HO,4N05,
+ SBiOa).
Sousazotate de bismuth.
20.
21.
22.
23.
24.
25.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
9.
10,
A basic nitrate (BiNO^.H^O or
Bi„03,NA.2H,0).
Sousazotate.
26. Basic nitrate (Bi„03,N„05,20H„, or
Bi" (N03)3,Bio03',30H;).
27. —
28. Azotate basique de bismuth (Bi'"
(AzO,) + H,0 or (BiO) AzO,
+ H„0).
29. Basic nitrate of bismuth, also called
trisnitrate of bismuth (Bi^Oj,
NA.H.O).
30. Wismuthnitrat. Bi(0N0„)(0H)2.
31. Basisches salpetersaures Wismuth
oxyd T^jj^logBi or NOjOBiO
+ H..0).
32. Basic nitrate (see 26).
33. Bismuthous subnitrate (Bi„03,
2HNO3).
34. Basic bismuth nitrate, Bi (OH)^
NO3.
35. Bismuthous nitrate dihydrate, NOj
(Bi"H020).
36. Basic bismuth nitrate, Bi(OH)2N03.
XI.
A subsalt.
A compound of
with chloride.
oxide of bismuth
(See 6.)
A subsalt (BiCl 1 2 BiO 1 HO)
Wismuthoxyd  chlorwismuth. Wis
muthoxychloriir. Basisch salz
saures Wismuthoxyd (BiClj,
2Bi03).
Basisches Salz.
(BiCl + 2BiH).
Wismuth Bisoxychlorid. Zweifach
basisches Wismuth Chlorid
(Bi„ei0j Oder Bi^eia + BiA)
Oxychloride of bismuth (BiCla +
2Bi03 + 3HO).
Oxychloride of bismuth (BiCl3,
2Bi03).
Oxychlorure de bismuth (Bi.,Cl3 +
2(Bi„03 + 3H0).
Oxysulphat of mercury.
Suboxysulphate of mercury.
Neutral persulphate of mercury.
Suboxysulphate of mercury.
Disulphate of mercury.
A subsalt.
A subsalt.
(HgO.S03 + 2HgO).
Schwefelsaures Quecksilberoxyd,
Drittel (SHgO.SOj).
XII.
19. Bisoxychlorid, zweifach basisches
Salz (2Bi03,BiCl3).
20. Oxychloride of bismuth (BiClj,
2Bi03).
21 (See 17.)
22 —
23. Oxychloride of bismuth (BiOCl),
1863. Bismuthyl chloride
(BiOCl), 1879. Supp. III.
24. Oxychlorure (BiOCl).
25. Basisches Chlorwismuth.
26. Oxychloride (BiClO).
27. Bismuth oxychloride (BiOCl).
28. Oxychlorure de bismuth (BiOCl or
Bi.,03,BiCl3).
29. Oxychloride of bismuth, 2(BiCl3,
Bi203),H„0.
30. Wismuthoxychloriir.
31. Basisches Chlorwismuth, Wismuth
oxycblorid (BiOCl).
32. Oxychloride (BiClO).
33. Bismuthous oxychloride, 2(BiCl3
Bi,,03),0H„ or BiOCl.
34. Bismuth oxychloride (BiOCl).
35. Bismuthous oxychloride (BiOCl).
36. Basic bismuth chloride. (Bismuth
oxychloride.)
1 1 . Basisches schwefelsaures Quecksilber
oxyd (SHgO.SOa).
12. Basisches schwefelsaures Quecksilber
oxyd.
13. Basisch schwefelsaures Quecksilber
oxyd (3HgO.S03).
14. Basisches schwefelsaures Queck
silberoxyd.
15. Basic sulphate (3HgO + SO3).
16. Subsulphate.
] 7. Sel basique (3HgO.S03).
ON CHEMICAL NOMENCLATURE.
273
'.SO3).
18. A basic salt (SRgO.SOj).
19. Drittelsaures Salz (3HgO.£
20. A subsalt (SHgO.SO,).
21. Sel basique (SHgO.SO').
22. —
23. Basic sulphate of mercury (SHgO.SOj
= HgSO,.2HgO).
24. Sel basique
25. —
26. A basic salt (SHgO.SOj).
27. A basic salt (HgjSOs).
28. Sulfate trimercurique(SOjHg,2HgO).
29. A basic sulphate (HgO.SO3.2HgO).
30. Drittelgesattigtes Mercuridsulfat.
31. Basisches Salz(SOj02Hg + 2HgO).
32. A basic salt (3HgO.S03).
33. A basic salt (HgS04.2HgO).
31. A basic salt (Hg3S06). „
35. Trimercuric sulphate (SHgOj).
36. Basic sulphate (SOj.OjHg + 2HgO).
10.
11.
12.
13.
14.
15,
16,
17,
xm.
18.
19.
Chlorosulphuret of mercury (hg +
2C)i2(hg + 2S).
Chloride and sulphuret of mercury
(HgCl + 2HgS).
C h 1 o r q u ecksilber Schwef elquecksil
ber, Oder Chlor und Schwefel
quecksilber (2HgS,HgCl).
SchwefelbasischesQuecksilberchlorid
(Berzelius' nomenclature) (HgClj
+ 2HgS).
Quecksilberschwefelchlorid (Hg€},
+ 2HgS).
Chlorosulphuret (HgCl + 2HgS).
Sulphochloride of mercury (HgCl,
2HgS).
HgCl + 2HgS,
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
Quecksilbers ul p huretochlorid
(Quecksilber chlorosulphuret)
(2HgS,HgCI).
(See No. 17.)
Sulphochloride of mercury (Hg.S,
cy.
Mercuric sulphochloride (HgjSjClj).
Sulfochlorure mercurique C2HeS,
HgCL).
Chlorosulphide of mercury (HgCl~
2HgS).
Mercuridthiochloriir.
(2HgS,HgCl,).
Trimercuric disulpho /HgClrr \
dichloride VHgCl^s^
36. —
1.
2.
3,
4.
5.
6,
7.
8.
9.
10.
11,
12.
13.
14,
15.
16.
Sulphoantimoniate.
Sulphostibias natricus (Na Sb2).
FiinfEachschwefelantimonnatrium,
Antimon persulphidNatriimi ( S ulpho
stibias natricus cum aqua) (Sb^Sj,
NaS + 12Aq) .
Natrium antimon Sulphid (3 NaS +
SbSJ.
AntimonpersulphidNatrium. Anti
monpersulphid  schwefelnatrium,
&c., &c. (Sb^Sj.NaS).
Sulphantimoniate (3NaS.SbS.),
1885.
XIV.
17.
18,
19,
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
Sulfantimoniate de sulfure
Sodium (3NaS.Sb2S3).
de
Natrium sulphantimoniat (3NaS,
SbSj).
Sulphantimoniate of sodium (3NaS,
SbS,).
Sulfantimoniate de sulfure de sodium
(SNaS.SbjSJ
Sulphantimonate of sodium (NaaSbS
or 3Na2S.Sb2S5).
Sulphantimoniates (Sb^S^SMoS or
SbS^M,).
Sodic sulphantimoniate (SbS^Naj).
Sulfoantimoniate de sodium (SbS.
Na3).
Sulphantimoniate.
Natriumthioantimonat (Na,SbSJ,
274
REPORT— 1885.
31. SbS^Naa, or (SbS) SaNa,.
32. Sodium sulphantimonate.
33. Trisodic sulphantimoniate (Na^SbS^).
34. Sodium thioantimonate (NajSbS,).
35. Trisulphosodic sulphantimonate (Sb
S"Nas3).
36. —
XV.
1.
2.
3.
4.
5.
6.
7.
8.
10.
11.
12.
13.
14.
16.
16.
17.
18.
19.
Fluat of potass and silica.
Fluate of potash and silica.
Fluosilicate of potash.
Silicofluate.
Fluosilicate of potash.
Silicofluoride of potassium (po + 2Si
+ 3f).
Silicofluoride of potassium (po + 2Si
+ 3f).
Double fluoride of silicon and potas
sium (2SiF3,3KF).
Fluorsiliciumkalium (KF,SiFj).
Fluorsiliciumkalium. Kieselfluor
kalium (SKF^/iSiFs).
Fluorkiesel Kalium.
KaliumKieselfluorid (3KF,2SiP3).
Fluosilicate of potassium, silico
fluoride of potassium (SiF^ + KF).
Double fluoride of silicon and
potassium (2SiF3,3KF).
Hydrofluosilicate de j^otasse (3KF1,
2SiFl3).
Double fluoride of silicium and
potassium (SKF.SiF,).
Kieselfluorkalium. Fluorkieselkalium
(3KaFl,2SiFl3, oder KaFl.SiFlJ.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
.35.
36.
Silicofluoride of potassium (KF,
SiF.).
Hydrofluosilicate de potasse (3KF1,
2SiFl3).
Silicofluoride of potassium. Potassic
silicofluoride (2KF,SiFj).
Fluorure double de sihcium et de
potassium.
Kieselfluorkalium.
Double fluoride of silicium and
potassium (2KF,SiFJ.
Potassic fluosilicate (K.jSiFg).
Fluosilicate de potassium.
Silicofluoride of potassium (2KF,
SiF,).
Metallsilicofluoriire.
Kieselfluormetalle (SiF^.MFj).
Double fluoride of silicium and
potassium (2KF,SiF,).
Potassic silicofluoride.
Silicofluoride. potassium fluosili
cate (K^SiFg).
Potassic silicofluoride (SiFjK2 = Si
F„2KF).
Potassium fluosilicate.
XVI.
1.
2.
3,
4.
5.
6.
7.
8.
10.
11.
12.
13.
14.
15.
16.
17.
Muriat of platinum and potass.
Muriate of platinum and potash.
Bichloroplatinate of potassium.
Platinobichloride of potassium
(pi + 2c) + (po + c).
Platinobichloride of potassium
(pl+2c) + (poic).
Chloride of platinum and jjotassium
(KCl + PtClj).
Zweifach Chlorplatinkalium (KC1 +
PtCU).
Kaliumplatinchlorid (KClj + PtClJ.
Kaliumplatinchlorid.
Kaliumplatinchlorid (KOi + PtGi^)
Platinchloridchlorkalium.
Double salt of bichloride of platinum
with chloride of potassium (KCl
+ PtCL).
Chloroplatinate of potassium (KCl,
PtClj).
Chlorure double de platine et de
potassium (PtCl, + KCl).
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
Bichloride of platinum and chloride
of potassium (PtClj.KCl).
Kaliumplatinchlorid. Kaliumchlo
roplatinat (KaCl.PtClj).
Double chloride of platinum and
potassium (KCl.PtCl,,).
Chlorure double de platine et de
potassium (PtCL i KCl).
Chloroplatinate of potassium, 1866.
potassium platinochloride (KjPt
CIJ. Supp. I. 1872.
Chlorure double de platine et de
potassium.
Kaliumplatinchlorid.
Potassium platinochloride (2KC1,
PtCl,).
Chloroplatinate de potassium.
Platinochloride of potassium (2KC1,
PtCl,).
Kaliumplatinchlorid.
Kaliumplatinchlorid (2KCl,PtCl4).
Potassium platinochloride or chloro
platinate (2KCl,PtCl<).
ON CHEMICAL NOMENCLATURE.
275
33. Potassic platinic chloride.
34. Potassium platinichloride or chloro
platinate (KjPtClJ.
35. Potassic platinic chloride (PtCl.,
2KC1).
36. Potassium chlorplatinate.
XVII.
1. —
2. —
3. —
4. —
5. —
6. Cyanuret of platinum and potassium.
7. —
8. Cyanuret of platinum and potas
sium.
9. Platinocyanide of potassium (K,
PtCy^ + SHO).
Einfachcyanplatinkalium (KCy,
PtCy).
10.
11.
12.
13.
U.
15.
16.
17.
18.
1.
2.
3.
4.
6.
«.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16,
17.
Kalium Platincyaniir (K6y, + Pt6y
+ 3H).
Kalium Platincyaniir (K6y + Pt€y
+ 3H0).
Platinocyanide of potassium (PtCy
+ KCy or K,Cpty).
Platinocyanides (MCy.PtCy).
Cyanure double de platine et de po
tassium (KCy + PtCy + 3H0).
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
Kaliumplatincyaniir
(3H0).
(KaCy.PtCy
XVIII.
18.
19.
20.
21.
22.
23.
Acetate and arsenite of copper,
CuO, (C^H303) + 3 (CuO.AsOj).
Essigarsenigsaures Kupferoxyd,
3(CuO,As03) + C^HjCuO^.
Essigsaures Kupferoxid und Arsenig
saures Kupferoxid, A,CuO
+ 3(As03, CuO).
Arsenichtsaures und essigsaiires
Kupferoxyd, (CuA + 3CuAs).
Arsenigessigsaures Kupferoxyd.
Compound of acetate of copper,
and arsenite of copper, CuO.A
f3(H0.2CuOhAs03).
Acetate and arsenite of copper, CuO,
(C^H303) + 3 (CuO.As,03).
Une combinaison, CuO. C.H3O3
+ 3(2CuO.AsO,).
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
Cyanure double de platine et de
potassium (KCy 1 PtCy t 3H0).
Platinocyanide of potassium (K..Pt
Cy^ = 2KCy,PtCy,), 1866. Potassic
platinous cyanide (KjPtCyJ.
Supp. I. 1872.
Plantinocyanure de potassium, (Pt
CyOK + 3H0.
Kaliumplatincyaniir.
Kaliumplatincyaniir (2KCy,PtCy2).
Potas.sium platinocyanide, K2Pt(CN).
+ I2H2O.
Potassium platinous cyanide.
Eine Verbindung, CuO.AcOj
+ 3(2CuO,A.s03).
CuO,CjH303 + 3 (CuO.AsOj).
CuO,C,H303 + 3 (2Cu0,As03).
Acetoarsenite of copper (CoHjOj)^
Cu", 3 (As02)2 Cu" or C^H.O*. Cu"0
+ 3 (AsACu"0).
Cupric acetoarsenite, Cu(As02)
(C2H3O2).
Un acetoarsenite.
Arsenigessigsaures Kupfer,
Cu.,(OAsO) 3 (OC2H3O).
Cupric arsenite and acetate,
SCuAsjOj. Cu (CjHjO^),.
Copper acetoarsenite, SCuASjO.
+ Cu(C2H302)2.
Double compound.
T 2
276 REPOET — 1885.
RepoH of the Committee, consisting of Professors Odllxg, Hunt
ington, and Hartley, ai^'pointed to investigate by means of
Photography the UltraViolet Spark Spectra emitted by Metallic
Elements, and their combinations under varying conditions,
Braxon up by Professor W. N. Hartley, F.R.S. {Secretary.)
The last Report of this Committee was presented at the Sotithport meet
ino of the British Association ; since then an investigation in detail has
bera prosecuted of the changes observable in photographs of the spectra
of the metals when a series of solutions of definite strengths is examined.
It had previously been shown that solutions containing the same element
in different proportions emit variations of the same spectrum, the lines
differing in number, length, and intensity ; and the converse— namely,
that under the same spark conditions similar solutions of the same
strength always emit the same spectrum. Furthermore, I have shown
the invariable character of the cadmium, tin, lead, and magnesium lines by
observations made on about five thousand photographs, including not
fewer than two hundred examples of other metals. The reason of this
arises from the fact that unless the spark be almost at the highest tempera
ture attainable, its emissive power is insufficient to affect the photographic
plate in the usual period of exposure ; it follows from this that when a
condenser of constant capacity is in circuit, variable conditions such as
may be introduced by the electrodes being near together or far apart, or
by the use of a large or small coil, do not affect the result. Sparks are
shortened and the character of the spectra is greatly altered by the use
of a coil with a stout secondary wire, an instrument introduced and
employed by M. Eugene Demarfay. The use of an instrument of this
kind is not well adapted to the photographic method of working, because
the nature of the sparks is such that the graphite electrodes are rapidly
burnt away and the sparks are very short.
For the examination of solutions chlorides are generally employed,
but sulphates and nitrates are also used. The electrodes are nearly
always of graphite (' Phil. Trans.' p. 52, Part I. 1884) ; sometimes gold,,
copper, or platinum electrodes are required for special purposes, wires of
the metal being twisted into wicks.
The solutions examined generally contained 1 per cent., ^i\ xrcrtn,
and ToW*^ °f metal. It is seldom that more than three or four lines
are visible in solutions of the latter dilution, and the rapidly diminishing
number of lines in solutions weaker than ^^ih per cent, is very striking.
In the following tables the spectra corresponding to various solutions are
given, and attention is particularly directed to the copper, silver, and tin.
spectra as illustrating this point. In many spectra it is impossible to
predict the line or lines which will be found to be the most persistent.
It ia also noticeable that the alteration of lines consequent on the dilution
of solutions is variable in character with different lines in the same
spectrum. Generally speaking, long lines shorten until they disappear,
sometimes they become attenuated before they shorten, and in other cases
they attenuate until they fade away altogether.
The calcium lines H and K attenuate considerably before they shorten,,
while the lines of copper with wavelengths 32732 and 32469, and of
silver, 33828 and 32801, attenuate and fade almost away before
shortening.
ON THE DLTBAVIOLET SPAEK SPECTRA.
277
Several examples could be quoted of the analysis of minerals made
by the spectroscope, the metallic constituents being estimated quantita
tively with exactitude and great faciUty. In some cases the results
obtained by the spectroscope inspire greater confidence than those made
by ordinary methods.
The descriptive tables which follow are intended to be used with
maps drawn to the scale of wavelengths, and to a scale of actual mea
surements taken from photographs, so that the lines may be readily
identified. The scale numbers given in the tables in hundredths of an
inch refer to photographs such as those published in the ' Journal of the
Chemical Society ' (' Trans.' vol. xli. p. 90, 1882), from which actual
measurements may be taken with an ivory scale.
The limit of sensitiveness of the spectrum reaction is perhaps the
greatest in the case of magnesium ; one part of the metal in 10,000
millions of solution is easily detected by the appearance of the lines with
wavelengths 2801 "6 and 2794"1 attenuated and shortened. By increasing
the strength of the spark the sensitiveness may be magnified 10,000 fold.
It was shown in the Report presented in 1883 how spectrum observa
tions may be applied to determining the atomic weight of an element.
Taking into account the spectrum of berylUam, this metal could find no
place among the triad elements, but naturally took a position at the head
of the dyad group. According to the periodic law its atomic weight
would thus have the value 9. This view was opposed at the time, but it
is satisfactory to learn that it has since been completely confirmed by the
experimental work of Messrs. Nilson and Pettersoa and Dr. Humpidge.
The Zinc Spectrum.
Scale numbers
Wavelengths
1 per cent.
01 per cent.
001 per cent.
Hundredths of an inch
10849
11375
11630
14569
19498
25231
26795
33444
33017
32817
30756
28001
25573
25015
33444
33017
32817
30756
28001 ?
25573
25015
33444
33017
32817
The Thallium Spectrum.
Scale numbers
Wavelengths
1 per cent.
01 per cent.
001 per cent.
Hundredths of an inch
6455
887
1430
17221
20187
25986
33527
37756
35186
30910
29177
27671
25300
22993
37756
.35186
30910
27671
25300
22993
37756
27671
278
EEPOET 1885.
The Cadmium Spectrum.
Wavelengths
Scale numbers
1 per cent.
01 per cent.
001 per cent.
0001 percent.
Hundredths of an inch
7937
/ 36120
\ 36096
36120
36120
7968
36096
36096
9430
/ 34667
\ 34652
34667
34667
9450
34652
34652
10145
34028
34028
1190
32602
20587
27477
27477
24824
25723
25723
3268
f 2321 6
23135
32985
23135
23135
33925
■ 22888
22658
22888
22888
34815
22658
22658
22658
37748
21964
4002
21468
The Aluminium Spectrum.
Wavelengths
Scale numbers
1 per cent.
01 per cent.
001 per cent.
0001 per cent.
Hundredtlis of an inch
f 4985
1.5116
/ 39609
.39609
39609
39609 ?
1.39434
39434
39434
39434 ?
The airlines conti;
^uous to the abo\
e are very strong, hence it is a little doubtful
whether they are pres
ent in the spectr
um of a solution so dilute as 001 per cent.
/ 7002
17105
f 371 34
137015
r 7917
1805
f36124
136011
36124
36124
36011
36011
8207
35844
r 142 86
1.1445
/ 30918
.30918
30918
.30918
1.30812
30812
30812
30812
1485
3056 6
19176
28153
28153
28153
28153
2263
26593
26593
22826
26512
26512
24966
25669
25669
30855
23733
3090
23720
3096
23702
30994
23672
31062
23645
The line with wavelengtli 3584"'4 is both much longer and stronger
than either 3612'6 or 36012, yet it is not so persistent. From appear
ing as a strong line it disappears rather suddenly.
The line v^ith wavelength 28153 is the strongest in this epectrum.
ON THE ULTRAVIOLET SPARK SPECTRA.
279
Tabular Description of the Spectra characteristic of Solutions
containing Magnesium.
Wavelengths of the lines visible
Scale numbers
Parts of magnesium per 100 of solution
10
1
01
003
002
001
0003
0002
0001
per cent.
per
per
per
per
per
per
per
per
cent.
cent.
cent.
cent. 1 cent.
cent.
cent.
cent.
Hundredths
of an inch
1746
4480
4480
4480
6930
r 38379
38379
38379^38379
38379
5983
■{ 38321
38321
38321*38321
38321
6007
38292
38292
38292
1423
r 30962
■I 30919
L 30899
30962
30962
14285
30919
30919
14318
30899
30899
1687
/ 29359
\ 29282
29359
29359
29359
29359 29359
29359
29359
29359
17018
29282
29282
29282
29282 29282
29282
29282
29282
18463
28512
28512
28512
28512
28512 28512
28512
28512
28512
19455
r28016
28016
28016
28016
28016 28016
28016
28016
28016
19539
I 27969
27969
27969
27969
27969 27969
27969
27969
27969
19595
' 27941
27941
27941
27941
27941 2794 1
27941
27941
27941
19692
[27896
27896
27896
27896
27896 27896
27896
27896
27896
19864
(27818
27818
27818
27818
1
19896
27802
1
1993
.' 27787
27787
27787
27787
27787 27787
19961
27769
19997
I27755
27755
27755
A line ma}' be shortened or weakened, but its wavelength in this table denotes
that although it may be changed it is still visible. The numbers bracketed are the
wavelengths of characteristic groups of lines.
The Indium Spectrum.
Scale numbers
Wavelengths
1 per cent.
01 per cent.
001 per cent.
Hundredths of an inch
1588
3991
11931
11968
15135
16800
17734
21456
25176
3322
45102
41013
32578
32555
30387
29408
28897
27093
25595
2307
45102
41013
32555
30387
29408
28897*
27093
2307
32555
30387
This is barely visible.
280
EEPORT — 1885.
The Copioer Spectrum.
Wavelengths
Scale numbers
1 per cent.
01 per cent.
001 per cent.
0001 per cent.
Hundredths of an inch
11310
33068
33068
11510
32899
r 11725*
/ 32732
132469
32732
32732
1 1207
32469
32469
32469
16453
29595
19013
28232
20136
27691
27691
2118
27212
21265
27] 84
27184
2137
27130
27130
2161 
27027
21658
27005
21937
26888
26888
2247
26667
23645t
26178
2411
25997
24158
25983
25594
25446
25446
26025
25288
25288
26100
25262
26677
25062
25062
27091
24914
27165
24891
27272
24856
27645
24732
29831
24033
2994
24001
r30917
\ 30957
/23716
123701
23716
23701
3368
22950
34367
22770
r35627t
r22482
22477
22482
j 3555
22477
] 3571
22440
22435
22440
L35732
22435
* This pair of lines differs from all others in the spectrum by not being shortened
on dilution, but becoming attenuated till at last they disappear. They remain long
lines till the last.
f This is a very fine and very long line.
X This group is distinctly seen to be composed of four lines in the photographs
of the 1 per cent, solution, and some lines, to the number of four or five, more
refrangible than these are visible.
ON THE ULTEAVIOLET SPARK SPECTRA.
281
The Silver Spectrum.
Wavelengths
Scale numbers
1 per cent.
01 per cent.
001 per cent.
0001 per cent.
Hundredths of an inch
10394
33823
33823
33823
11645
32801
32801
32801
1685
29376
1693
29335
29336
17017
29282
29282
17502
29016
17607
28956
18044
28727
28727
19182
28145
19503
27988
20181
27664
27664
2042
27555
21422
27113
27113
22627
26596
26596
22708
26562
2463
25799
26881
25060
25060
27452
24799
27541
24768
27641
24733
24733
27992
24622
28052
24598
2826
24530
28438
24474
24474
28746
24373
24373
24373
2900
24298
24298
29308
24199
24199
29535
24133
24133
24133
24133
29594
24113
24113
29794
24064
29885
24045
30110
23957
30274
23908
30407
23867
30525
23836
30794
23765
31170
23643
31234
23623
31347
23592
23592
31388
2358
23580
32335
23317
23317
23317
32573
23253
23253
23253
32737
23205
23205
23205
32859
23174
23174
23174
34255
22807
22807
35495
22499
22499
35490
22476
22476
22476
36286
22306
282
REPORT 1885.
The Mercury Spectrum.
Scale numbers
Wavelengths
1 per cent.
01 per cent.
001 per cent.
Hundredths of an inch
r 746
< 7537
L 7737
r 13708
i 13795
16337
18545
25875
36451
f 36629
{ 36544
L36329
/31304
131245
29664
28468
25338
22257
36329
31304
29664
25338
25338
The Tin Spectrum.
Wavelengths
Scale numbers
1 per cent.
01 per cent.
001 per cent.
Hundredths of an inch
6240
38003
38003
ri0751
'33518
J 33299
33518
1 11025
33299
1 11603
' 32829
32616
32829
tll883
32616
1307
31743
31743
/15218
115629
/ 30330
130079
30330
30079
17305
29120
17618
28950
1778
28869
ri8247
r28620
28620
28620
\ 18499
{ 28492
Ll8701
L28339
28339
1923
28125
28125
19828
27840
19934
27788
27788
21535
27058
27058
27058
' 22495
'26642
22598
26606
22656
26579
26579
t
22967
*
26454
23023
26432
26432
23317
26314
26314
'24265
"25936
24310
25917
24870
25705
25705
25545
25456
25456
r2698
12734
f 24950
124829
24829
/ 28995
129237
/ 24293
124218
24293
24293
24218
31011
23683
31485
23550
23550
32194
23353
32834
23179
35583
22470
ON THE IJLTEAVIOLET SPARK SPKCTEA.
283
The Lead
Spectrum.
Wavelengths
Scale numbers
1 per cent.
01 per cent.
001 per cent.
Hundredths of an inch
4293
40575
40575
6761
37389
37389
7269
36829
36829*
768
36392
36392
8331
35726
35726
35726
17045
28722
28722t
18837
28322
28322
19030
28221
22541
26625
26625
23748
26134
26134
24708
25764
37343
22043
The Tellurmm Spectrum.
Wavelengths
Scale numbers
1 per cent.
01 per cent.
001 per cent.
Hundredths of an inch
1039
33824
33824
11643
32800
32800
11735
32734
32734
12077
3246 8
32168
32468
17624
28943
18125
28677
1834
28570
3441
23863
23863+
30492
23838
23838t
35518
22480
35536
22473§
35718
22433
The Arsenic Spectrum.
Wavelengths
Scale numbers
1 per cent.
01 per cent.
001 per cent.
Hundredths of au inch
»
18304
28597
19922
27795
27795
3166
23501
33914
22889
This is an exceedingly poor spectrum.
* Barely visible. f Very faint.
X These lines appear very distinctly and are continuous in a 1 per cent, solution.
§ The two last lines are faint, 22433 exceedingly so.
284
REPORT — 1885.
The Antimony Spectrum.
Scale numbers
Wavelengths
1 per cent.
01 per cent.
001 per cent.
Hxmdredths of an inch
6763
8074
9021
10936
11821
1208
12287
15291
17929
19705
24165
26033
33037
37390
35978
35046
33364
32666
32466
32316
30290
28771
27896
25972
25276
23118
28771
27896
25972
25276
28771
25972
The Bismuth Spectrum.
Scale numbers
Wavelengths
1 per cent.
01 per cent.
001 per cent
Hundredths of an inch
631
7163
8099
8969
984
10225
14685
15375
15898
15967
16852
17585
18391
18549
29466
37927
36953
35957
35105
34309
33967
30671
30238
29922
29881
29375
28972
28548
28461
24148
30671
30238
29921
28972
28548
28461
30671
Report of the Committee, consisting of Professor Tilden, Professor
W. Ramsay, and Dr. W. W. J, Nicol {Secretary), appointed for
the pxLrpose of investigating the subject of Vapour Pressures and
Refractive Indices of Salt Solutions.
I. Molecular Volumes of Salt Solutions. Part 11.^
The molecular volumes have been determined of fiffcysLx solutions,
comprising fortyseven salts of potassium, sodium, lithium, strontium,
cadmium, cobalt, and nickel, with chlorine, bromine, chloric, carbonic,
sulphuric, nitric, orthophosphoric, metaphosphoric, acetic, oxalic, tartaric,
• Published in PMl. Mag., 1884.
VAPOUR PEESSUBES AND REFEACTIVE INDICES OP SALT SOLUTIONS. 285
and citric acids. The previous results were completely confirmed.
The law is as follows : —
The molecular volume of a salt in dilute solution is a quantity com
posed of two constants, one for the metal and another for the salt radical.
It follows that the replacement of one metal, or salt radical, by another
metal, or salt radical, is always attended by the same volume charge no
matter how they may be combined together.
The presence or absence of water of crystallization in one or both of
the salts has no effect on the above law ; it therefore follows that it has
the same volume as_ the solvent water. Water of constitution, however,
shows itself in solution by possessing a volume markedly different from
that of the rest of the water.
These results point to the presence in solution of what may be
termed the anhydrous salt, in contradistinction to the view that a
hydrate, definite or indefinite, results from solution ; or, in other words
no part of the water in solution is in a position, relative to the salt',
different from the remainder. '
II. Saturation of Salt Solutions. Part II.
It is found that the molecular volumes of a series of solutions of
different strengths of the same salt may be satisfactorily expressed bv
the formula : — ''
M. V. = 1800 + na + n'^ji  n^y.
Where n = number of molecules of salt per 100 HgO, and a, 3 and y
constants depending on the salt, '
r = na + n^j3 — n^y •
and
7*
 = a + 7i/3 — n^y.
n
This last is the mean molecular volume of the salt in solution. The
curve is a parabola, and is such that ^ = twice the solubility of the salt
in question .'. i^ = solubility ; but this is also the apex of the parabola ^
saturation is therefore reached when the further addition of salt would
produce dimmution of the mean molecular volume of the molecules
already present. The last molecule before saturation, enters into solution
with a volume sensibly equal to the mean, as is shown thus .
(«« + n^^  n^y)  ((n  l)a + {n 1)^/3  (» _ 1)3^) ^ „ ^ ,^^ _ ^^2^^
When n = 'l±l.
2y
III. Supersaturation of Salt Solutions.^
In these papers experiments are described which lead to the con
clusion that the only truly supersaturated solutions are those which
result from the fact that, when a hot solution is cooled, a finite time?
IS required for the excees of salt to crystaUize out— what is usually
' Published (1) Phil. Mag., June, 1885 ; (2) Phil. Mag., September, 1885,
286 REPORT — 1885.
termed supersaturation is not really so at all. Thus a distinctly super
saturated solution of sodium sulphate readily dissolves a quantity of
the dehydrated salt when brought in contact with it without access
of air. This sliows that the solution is not even saturated, much less
supersaturated ; still this may be explained by the supposition that the
constitution of a supersaturated solution is not the same as an ordinary
one, inasmuch as heat is necessary for its preparation; the effect of
heat being to decompose the decahydrate, no union of water and salt
taking place in cooling. In the second paper it is shown that this
is entirely a mistake. Supersaturated solutions are readily prepared
in the cold by simply enclosing the dehydrated salt in a bulb, placing
this in a bottle with the proper quantity of water, and, after closing,
heating the bottle to 100° for a few minutes. When the whole is cold,
the bottle is shaken, the bulb broken, and the salt readily dissolves. If
excess of salt be used, the solution has the same percentage composition
as one prepared by heating the decahydrate, and allowing it to cool with
the excess of salt to the same temperature, air being excluded. It is
further found that when the dehydrated salt is brought in contact with
the water, as above described, no caking together is observable, the
powdery condition being ietained till solution is complete. Thus there
is no hydration previous to solution, as is indeed shown by the possibility
of preparing supersaturated solutions in this way, for were the smallest
trace of the decahydrate produced such a solution, could not be formed.
During the act of solution, however, considerable heat is evolved, which,
as shown above, cannot be due to hydration, but may possibly result
from the enormous contraction, about 40 per cent., undergone by the
fialt.
Finally, density determinations of solutions of Na2S04 and Na2S203,
of various strengths, show that in passing the ordinary saturation point
there is nothing to indicate any change in the constitution of the solution.
The molecular volume steadily increases from the most dilute solution
up to the most concentrated supersaturated solution examined, exactly
as it does with an ordinary solution which is not capable of super
saturation.
From these and other experiments it follows that a socalled super
saturated solution is simply a saturated or nonsaturated solution of
the anhydrous salt ; that any solution of a hydrated salt contains no
hydrate of that salt, but that it is at the moment of crystallization that
^combination of the water and salt takes place.
IV. Vapoiir Pressures of Salt Sohdions. 1. Boiling Points of
Saturated Solutions.^
The method of experiment was to measure the pressure under which
■a saturated solution of the salt boiled at a definite temperature.
The experiments included determinations at 65°, 75°, 85°, and 95° for
NaNOs, KNO3, NagCOa, K2CO3, MnS04, FeS04, and the results are
expressed in terms of degrees of rise of boiling point. This is found
to be a quantity increasing with the temperature when the solubility
increases ; on the other hand, it decreases when the solubility diminishes
with rise of temperature.
It is preferable, however, to express the effect of salt on the
» Published PMl. Mag., October 1885.
VAPOUR PRESSURES AND REFRACTIVE INDICES OF SALT SOLUTIONS. 287
1 — p^
vapour pressure of water by the value — i ; where p = pressure of
vapour of pure water, p^ := pressure of water vapour from salt solution
containing 71 molecules per 100 H2O, and this, as was to be expected, is
in all cases a diminishing quantity with rise of temperature — showing
that, in a constantly saturated solution, a salt exercises a less restraining
effect on the water the higher the temperature.
2. Vapour Pressure of Water from Nonsaturated Salt Solutions.
The experiments on this subject are not yet complete, but are suffi
ciently advanced to justify certain conclusions regarding the behaviour
of salts under varying conditions of temperature and concentration.
The method employed was the same as that in the previous section,
with this difference, that a dilute, not a saturated, solution of the salt
was employed, and successive portions of water were distilled off and
weighed. In this way the concentration at different pressures and at a
definite temperature was readily determined.
Four salts have, as yet, been examined, NaCl, KCl, NaNOg, and
KNO3. The temperature chosen was 70°, though some experiments
were made at 90°.
Two of the above salts have been examined in solutions of constant
strength at temperatures of 70°, 75°, 80°, 85°, and 90°.
The general results are as follows : —
(a) When temperature is constant and n varying, then P~P
n
increases with increase of n in the case of NaCl ; is constant, or nearly
fio, with KCl, and diminishes more or less rapidly with NaNOg and
KNO3. These results are fully confirmed by Tammann's results, obtained
by the Barometric method (Wiedem. Ann. 24), a close agreement being
found between the two sets of figures.
(/3) When the concentration is constant but temperature varying,
then the value of ^_i_ or 1 — ^ is a diminishing one with NaCI and
pn pn
a slowly increasing one in the case of the other three salts. This also is
confirmed by Tammann's results, and general agreement is to be found
with the experiments of Legrand (18.35), conducted in an entirely
different way.
It is believed that there is an intimate connection between this
behaviour of the salts and their solubility, but the discussion of this
question is postponed till the results are more numerous and complete.
V. Expansion of Salt Solutions.
The dilatation of solutions containing definite numbers of molecules
1, 3, 5, or 2, 4, 6, Ac, of NaCl, KCl, NaNOj, and KNO3, have been
determined by means of specially constructed dilatometers, and a special
constant temperature bath, by means of which a tube 700mm. lono can
be kept for any length of time at a definite temperature, the tempera
ture of the one end differing from that of the other not more than 0°l.
Thus all necessity for correction of the results for the exposed portion of
the stem of the dilatometer is avoided.
As in the previous section, the experiments are not yet complete, but
have fully established the following conclusions : —
288 EEPOBT— 1885.
(a) The expansion of a salt solution is the more nniform the more
concentrated it is. The curves representing the expansion approach more
nearly straight lines as n increases.
(/3) At low temperatures salt solutions expand more than water, at
higher ones less ; there is thus a point at which the coefficient of expan
sion is the same as that of water. This temperature is little, if at all^
affected by the concentration. They are as follows : —
NaCl
. 55° 60°
KCl
. 50° 55°
NaNOa •
. 80° 100°
KNO3 .
. 75° 80°
(y) The volumes at different temperatures may be satisfactorily ex
pressed by interpolation formulte of the form
V= 100,000 + ra + i'2/3;
Where t'=t°—20°, and a and /3 constants depending on the salt and the
value of n. In 126 determinations only two differed from the calculated
value by more than ., ~.^^ , the mean error being less than ~^
100,000 ^ 100,000
The constants a and /3 are thus related ; as n increases a increases, but /3
decreases ; the expansion approximating more and more to 100,000 + a t'^
The results confirm in most points those of Kremers, and it is hoped
when the experiments are complete that it will be possible to establish the
connection between the vapour pressures and the molecular volumes, aa
has already been attempted by Tammann in an incomplete form.
Rejport of the Committee, consisting of Professor Sir H. E. RoscoE,
Mr. J. N. LocKYER, Professors Dewar, Wolcott Gibbs, Liveing,
Schuster, and W. N. Hartley, Captain Abney, and Dr. Marshall
Watts {Secretary), appointed for the purpose of preparing a new
series of Wavelength Tables of the Spectra of the Elements and
Compounds.
The present Report contains the completion of the tables of the spectra
of the elements, and a portion of those of the spectra of compounds.
The measurements are given in tenmillionths of a millimetre (or tenth
metres), and are based upon the measurements of the Fraunhofer lines
by Angstrom for the whole visible rays, and the extension of the same
series of measurements into the ultraviolet portion of the spectrum made
by Cornu and other observers. It will be well to repeat here the funda
mental values of wavelength of the chief solar lines. The small correc
tions indicated at page 29 of Angstrom's Memoir, ' Le Spectre Normal
du Soleil,' have been applied to his numbers — but they are uncorrected
for the dispersion of air. Hence the numbers in the tables represent
wavelengths in air, of 760°^™ pressure at Upsala, and 16° C. temperature.
The numbers taken from Thalen's 'Determination des Longueurs d'Onde
des Raies Metalliques ' in the same way have had applied to them the
necessary small corrections to bring them into harmony with the numbers
finally adopted by Angstrom as ' Yaleurs definitives ' (pp. 25 and 3132).
ON WAVELENGTH TABLES OF THE SPECTRA OF THE ELEMENTS. 289
Feaunhofbb Lines
A .
B .
C (H). .
D (Na)
E (Ca & Fe)
b, (Mg) .
\ (Mg) .
b3 (Ni & Fe)
b, (Mg&Fe)
F (H)
G (Fe)
H (Ca)
K (Ca)
L (Fe)
M (Fe)
N (Fe)
O (Fe, double)
P (Fe & Ti)
Q (Fe)
E (Fe & Ca)
r (Fe, double)
S, (Ni, double)
Sj (Fe, triple)
s (Fe)
T (Fe, double)
t (Fe)
U (Fe)
589212
76040
68670
65621
/ 589513
\ 588912
526913
518310
517216
516848
516688
486072
430725
39681
39330
38198
37270
35805
34398
33592
32849
31790
31443
31006 \
30095/
30464
30197
29943
29478
31000
The following symbols are employed in the tables to indicate the
character of the lines :
s denotes that the line is sharply defined.
n denotes that the line is illdefined or nebulous.
b denotes a band, the position of the brightest part being given.
b' denotes a band sharply defined on the least refracted side, and fading away
towards the blue,
b' denotes a band sharply defined on its more refracted side, and fading away
towards the red.
The width of a broad band is sometimes indicated by a suffix, giving
the width in ninthmetres; thus, 4997 Vj means that the bright edge of
the band is the 4997, and that it fades away above 4947 ; whereas 6532 b4
means that the band extends from 6552 to 6512, its brightest point being
at 6532.
denotes that the line is continuous.
d denotes that the line is discontinuous, or a ' short * line.
r denotes that the line is frequently ' reversed.'
A number within parentheses, thus : (30919), means that while a Une in this
position has been observed, no new measurements of wavelength was made
— the wavelength being quoted from another observer.
The intensities of the lines are expressed upon an ascending scale
from 1 to 10 ; 1 being the feeblest and 10 the brightest.
1885.
290
EEPOET 1885.
WAVELENGTH TABLES OF THE SPECTRA OF
THE ELEMENTS.
Sulphur.
I. Band
Spectrum
II. Line
Spectrum
Intensity
and Character
Salet
o
Angstrom
Hasselberg
PlUcker and
Hittorf
i
Salet
I.
II.
6579
2
6454
2
6421
4
6404
6400
8
6390
6390
6
6321
6325
8
6309
6310
8
6290
6290
10
6145
6152
lb'
2
6090
6111
lb
2
6030
6009
lb
4
5970
2b'
5900
6866
2b'
4
6845
5810
2b'
4
5780
6780
2b'
4
5715
2b'
5671
5667
■5670
6
56597
5657
5650
5660
5655
8
8
5645
5645
56393
5641
5618
a *
5647
3b'
10
4
5613
56038
5609
5610
10
5595
5584
3b'
4
55613
5568
5558
5570
8
4
8535
55169
5532
5522
3b'
2
4
55073
5.508
5510
8
5480
3b'
5474
54705
5473
f 5477
8
5451
54510
5452
fi< *5455
10
5432
54381
5438
L 5432
8
5425
54297
54184
53866
5425
3b'
6
5365
5b'
5345
53417
5338
f5350
10
6310
5322
53192
52178
5304
5269
5231
5218
^ L5320
2b'
10
2
4
2
6250
5207
5207
/5220
L5217 U
8b'
8
8
6190
6191
52144
52001
5199
5191
5182
5205 J
5160
8b'
10
2
10
5143
51425
5143
5141
2b'
6
2
5140
2
ON "WAVELENGTH TABLES OF THE SPECTRA OF THE ELEMENTS. 291
Sulphite — cantinued.
1
I. Band
Spectrum
II. Line Spectrum
Intensity
and Character
Salet
o
Angstrom
Hasselberg
Pliicker and
Hittorf
Salet
I.
IL
5124
4
5110
2
5088
61029
5078.3
5096
5068
5103
8b'
8
2
5040
50449
5044
5036
Sb"
4
2
5027
50325
/5030
1.5024
f5030
5024
10
10
5013
50127
f5013
5013
8
\ 5004
5003
e
6008
8
2
4990
4994
49939
roOOO
\4990
5O0O
6b'
4
.4990
6
4945
49415
4942
6b'
4
4926
4925
49185
49019
4924
4922
4902
C4925
8
6
6
4890
48845
4884
2b
6
4840
4825
4825
8b'
6
48156
4813
7?4810
8
48085
4804
4
4793
47928
47785
47628
47528
4791
4777
4768
4762
7b'
4
2
2
2
4755
4734
4723
2b'
2
2
47149
4718
04715
8
4705
4692
4671
4690
4670
5b'
b
b
4655
4657
4630
4655
4630
6b'
b
b
4615
4610
4593
4580
4561
4610
4590
4580
4560
8b'
b
b
b
b
45515
4552
4556
10
4540
2b'
45247
4323
4525
10
44851
4485
M'
4485
10
4470
8b'
44640
4466
4467
10
4450
4432
4422
4435
4425
2b
b
b
4367
4386
4358
4330
4343
4336
4329
4390
3b
b
4
4
4
4
4
4320
2b
4315
4315 1
b
U2
292
REPORT — 1885.
Sulphur — oontimied.
I. Band
Spectrum
II. Line Spectrum
Intensity and
Character
I. Band
Spectrum
II. Line Spectrum
Intensitj' and
Character
Salet
Plucker i c„, .
& Hittorf S*^^^*
I.
II.
Salet
Plucker
& Hittorf
Salet
I.
II.
4297
4284
4279
4272
4259
4255
4241
4229
T<
4295
4282
4269
.4250
8
8
4
8
4
8
b
b
4187
4070
4196
4181
4168
4158
4140
4192
f 4180
p{ 4162
L4155
2b
2b
b
6
8
6
6
2^
* Double.
Tantalum.
Arc Spectrum
Intensity
and
Character
Arc Spectrum
Intensity
and
Character
Arc Spectrum
Intensity
and
Character
Lockyer
Lockyer
Lockyer
.39986
39957
39950
39910
39874
39797
39755
39730
39716
39712
39645
39633
39427
39403
39363
39140
39110
390G9
Tellurium.
I. Band
Spectrum
II. Line Spectrum
Intensity an
d Character
Salet
Salet
Huggins
6645
Thale'n
I.
4
(6437)
6431
6366
6347
6290
64372
10s
Is
In
2?
6250
6243
6228
5b
3n
3s
6150
5b
6050
(6046)
6042
60462
5b
6sd
(6012)
6010
5995
60127
6sd
In
(5973)
5970
59732
lOsc
5940
(5935)
5934
59352
5b
8sc
(5856)
5854
58566
4sd
5855
(5852)
5849
58521
7b
4sd
(5825)
58251
4nd
(5805)
58056
57811
4nd
6sd
(5755)
5756
57551
lOsc
5740
57411
2sd
5735
8b'
(5707)
5708
57066
lOsc
5685
8b
(5647)
5646
56471
lOsc
5618
56161
4sd
(5574)
5675
55741
8sc
5560
4b
(5488)
5486
54880
6sd
ON "WAVELENGTH TABLES OF THE SPECTRA OF THE ELEMENTS. 293
Tellurium — continued.
I. Band
Spectrum
II. Line Spectrum
Intensity and Character
Salet
Salet
Huggins
Thale'n
I.
n.
5470
(5477)
5476
54776
4b
6sd
(5447)
5447
54476
Ssc
5410
5409
54086
4b
4sd
(5366)
5366
53661
6sc
5340
4b
(5310)
5309
53101
6sd
5298
52991
2sd
5278
4b
5220
(5217)
5222
52172
51722
4b
8nc
2sd
5156
(5152)
51522
4b
6sd
5134
51332
2nd
(5104)
51041
6sd
5070
4b
5038
50351
4sd
5015
4b
4970
4b
4920
48951
4b
2nd
4870
(4866)
4866
48666
4b
4nd
4832
48321
2nd
48W
4b
^o—v
Hartley
4785
47851
2nd
4767
and Adeney
8b
4725
8b
47075
4709
4sd
46930
4sd
4670
4664
4652
8b
In
In
4600
46020
4602
4599
46036
6b
2sd
In
4560
4544
6b
b
4510
/44870
\ 44800
6b
2sd
4479
2sd
4470
44360
4b
2sd
4400
44000
43780
43645
4b
2sd
2sd
2sd
4350
43530
4352
2b
2.sd
4330
43246
2b
4sd
43015
4302
6sd
4280
r42927
\ 42873
42744
2b
4sd
4sd
6sd
42598
4259
6sd
4250
42211
2b
6sd
4200
r 41807
\41703
2b
2sd
4sd
4150
41197
40727
2b
4sd
2sd
40613
4063
Csd
294
RBPORT 1885.
Tellurium — continued.
Line Spectrum
Intensity
and
Character
Line Si)ectrum
Intensity
and
Character
Line Spectrum
Intensity
and
Character
Hartley
Hartley
Hartley
and Adeney
and Adeney
and Adeney
^I^AAlrAA lt,V^bX^4
40542
6sd
332:>7
4sd
29234
4sd
40483
4sd
33158
4sd
29189
2sd
40060
8sd
33071
8sc
29059
2sd
39838
6sd
32896
2sc
29019
4sd
39686
6sd
/ 32800
lOsc
/28943
\ 28933
Snd
39480
6sd
1.32734
lOsc
6sd
39325
2sd
/ 32674
\ 32646
2sd
/ 28774
\ 28736
2sd
39087
2nd
2sd
2sd
38413
8sd
32563
Ssd
f28677
s' 28599
[28570
Snd
38030
4sd
32508
4sd
6sd
37969
2sd
32168
lOsc
Snd
37890
4sd
32421
4sd
/ 28449
1 2840
6sd
37760
4sd
; 32342
4sd
6sd
37710
4sd
\ 32294
2sd
; 28369
128344
2sd
37650
4sd
32218
4sd
2sd
37590
4sd
32176
4sd
28232
6sc
37540
4sd
32133
4sd
[28153
2sd
37355
Ssd
32104
2sd
\28130
2sd
37262
Ssd
31922
4sc
f 27991
4sd
37160
4sd
31881
4sc
■{ 27956
4sd
36987
4sd
31837
2sd
L27919
Snd
36833
4sd
31744
4sc
f 27686
6sc
36767
4sd
31685
4sd
<^ 27665
6sd
36704
4sd
31584
2sd
[ 27660
4sc
36564
4sd
31541
4sd
27560
2sc
/ 3649 2
\36443
6sd
31457
4sd
27515
2nd
6sd
31317
2sd
r27450
\27430
4sd
36363
4sd
31247
2sd
4sd
36267
4sd
31195
4nd
/ 27395
L 27380
4sd
36170
6sd
31075
6sd
4sd
36110
4sd
30987
4sd
f 27232
■{ 27207
L27I8O
2nd
36017
4sd
30955
4sd
2sd
35996
4sd
308S0
4sd
2sd
35